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User:ColorfulGalaxy/Encyclopedia of numbers
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__NOTOC__ This article is inspired by [http://mathigon.org/almanac this] article, which was biased towards decimal properties and did not mention imaginary numbers. This article, instead, is biased towards septenary and tetradecimal properties, though the numbers are written in decimal. [[Shidinn language|Shidinn]]-related entries, including those notable noticed by other Shidinn enthusiasts, are also welcome. Readers may try to verify these as an exercise. If there is something wrong, please [[User talk:ColorfulGalaxy/Sandbox|contact the author]]. {| border="0" class="toccolours wikitable" |- ! colspan="10" | {{MediaWiki:Toc}} |- | align="center" | [[#0|0]] || [[#1|1]] || [[#2|2]] || [[#7|7]] || [[#14|14]] || [[#49|49]] || [[#196|196]] || [[#343|343]] || [[#2401|2401]] || [[#2744|2744]] __NOTOC__ |- | align="center" colspan="10" | [[#top|Top of page]] — [[#Legend|Legend]] — [[#See also|See also]] — [[#External links|External links]] |} ==Legend== <div style="border:2px solid blue;">Positive prime numbers </div> <div style="border:2px solid magenta;">Number (excluding positive prime numbers) whose absolute value is an integer</div> <div style="border:2px solid orange;">Number whose absolute value is a rational number that is not integer</div> <div style="border:2px solid cyan;">Number whose absolute value is an algebraic irrational number</div> <div style="border:2px solid green;">Number whose absolute value is a transcendental real number</div> <div style="border:2px solid red;">Unknown/approximation</div> Some terms can have subscripts. They indicate which base<ref name="base"/> the property applies in. For example, "digit<sub>14</sub>"<ref name="digit"/> is read as "tetradecimal digit". ==Numbers== ===0=== <div style="border:2px solid #ff00ff"> * ... is the smallest non-negative number. * ... is the additive identity. * ... is the number of two-digit<sub>7</sub><ref name="digit"/> prime numbers that are both "emirp<sub>7</sub>"<ref name="emirp"/> and Mersenne. * ... is the number of two-digit<sub>7</sub><ref name="digit"/> prime numbers that are neither "emirp<sub>7</sub>"<ref name="emirp"/> nor Mersenne. </div> ===1=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive number. * ... is the multiplicative identity. * ... has a Shidinn letter shaped like it: [[Shidinn letter 1]] * ... percent is approximately the relative frequency of three-letter palindromic Shidinn words among all Shidinn words (not counting legacy spelling). * ... is the only digit<sub>14(za)</sub><ref name="digit"/><ref group="note" name="za14"/> with an ascender pointing at the top left corner. (citation needed) </div> ===2=== <div style="border:2px solid blue"> * ... is the smallest positive prime number. * ... is the only even positive prime number. * ... is an RDI<sub>7</sub><ref name="rdi"/> of order 2. * ... is the last distinct digit<sub>7</sub><ref name="digit"/> to encounter when the digits<sub>7</sub> of π are scanned<ref name="constantdigitscanning"/>. * ... is an honest number<ref name="honest"/> in Shidinn. </div> ===3=== <div style="border:2px solid blue"> * ... is the smallest odd positive prime number. * ... is the smallest Full Reptend Prime<sub>14</sub><ref name="frp"/>. * ... percent is approximately the relative frequency of five-letter Shidinn words among all Shidinn words (not counting legacy spelling). </div> ===π=== <div style="border:2px solid green;"> * ... contains almost everyone's birthday in 6-digit or 8-digit form. * ... is the irrational number that we most known. * ... is shaped like the middle case form of the [[Shidinn letter N]]. </div> ===4=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive composite number. * ... is the 2nd smallest positive square number. * ... is the number of two-digit<sub>14</sub><ref name="digit"/> repdigit<sub>14</sub><ref name="repdigit"/> triangular numbers. * ... is the largest known positive integer ''n'' such that there exists an arithmetic progression with ''n'' terms (all positive, indexed 1 through ''n'') satisfying the fact that the number of positive factors each term has is exactly equal to the term's index. * ... has a Shidinn letter shaped like it: [[Shidinn letter 4]] * ... percent is approximately the relative frequency of two-letter Shidinn words among all Shidinn words (not counting legacy spelling). </div> ===5=== <div style="border:2px solid blue"> * ... is the smallest positive odd number that is not a repunit<sub>2</sub><ref name="repunit"/> number. * ... is the number of Platonic solids. * ... is the number of letters in the longest word in Shidinn. There are 278 known five-letter words. * ... was the number of members in the Shidinn community administration committee when it started. * ... consecutive digits<sub>7</sub><ref name="digit"/> immediately after the point in π are multiples of 3. </div> ===6=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive composite number that is not a perfect power. * ... is the largest digit<sub>7</sub><ref name="digit"/>. * ... is the smallest perfect number. * ... is the smallest positive integer value of ''n'' such that the digits<sub>7</sub><ref name="digit"/> of ''n'' are all even, while the digits<sub>7</sub> of ''n''<sup>2</sup> are all odd. * ... is the smallest strobogrammatic<sub>14(za)</sub><ref group="note" name="za14"/> non-negative integer. Note that 0 is not strobogrammatic in this writing system. * ... has a Shidinn letter shaped like it: [[Shidinn letter 6]] * ... , as 3 plus 3, is an honest number<ref name="honest"/> in Shidinn. * ... is the smallest positive integer that is not a self-ranked<sub>10</sub><ref name="a108968"/> number in Shidinn, although it used to be a self-ranked<sub>10</sub> number in Shidinn. * ... is the number of known Shidinn characters with [[希顶解经|gematria value]] of exactly 100000. </div> ===7=== <div style="border:2px solid blue"> * ... is the third smallest repunit<sub>2</sub><ref name="repunit"/> number. * ... is the smallest positive two-digit<sub>7</sub><ref name="digit"/> number. * ... is the second smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> number. * ... is the numerator of a fractional Friedman<sub>14</sub><ref name="almostfriedman"/> number: '''7'''/5 = (8-1)/5 ≈ 1 + 5×14<sup>-1</sup> + 8×14<sup>-2</sup> * ... is the smallest positive strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number. * ... is the number of classical elements in Shidinn culture. See [[Seven elements]]. * ... is the unique positive integer ''n'' such that "the smallest integer ''m'' such that e<sup>''m''</sup> exceeds ''n''<sup>''n''</sup> is exactly equal to 2''n''". * ... is the smallest positive non-unity integer ''n'' such that there exists a two-digit<sub>n</sub><ref name="digit"/> narcissistic<sub>n</sub><ref name="narcissistic"/> square number. * ... is the smallest positive non-unity integer ''n'' such that there exists a four-digit<sub>n</sub><ref name="digit"/> repdigit<sub>n</sub><ref name="repdigit"/> square number. * ... is the smallest known positive non-unity integer ''n'' such that there exists a three-digit<sub>n</sub><ref name="digit"/> number k=a×n<sup>2</sup>+b×n+c satisfying that k-1, k and k+1 have a, b and c (i. e. its digits) positive factors respectively. * ... , as 5 plus 2, is an honest number<ref name="honest"/> in Shidinn. * ... is the number that represents God in western culture. </div> ===8=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive composite cube number. * ... is the smallest positive composite Fibonacci number. * ... is the largest cube in the Fibonacci sequence. * ... is the second smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... is the smallest known repfigit<sub>7</sub><ref name="repfigit"/> number. * ... is the third smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> number. * ... is the numerator of a "nice" fractional Friedman<sub>14</sub><ref name="almostfriedman"/> number: '''8'''/5 = 1×8/5 ≈ 1 + 8×14<sup>-1</sup> + 5×14<sup>-2</sup> * ... is the second positive cubic number. </div> ===9=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive odd composite number. * ... is the second smallest Smarandache<sub>7</sub><ref name="smarandache"/> number. * ... is the smallest Early Bird<sub>7</sub><ref name="a116700"/> number. * ... is the smallest positive integer ''n'' such that 3<sup>''n''</sup> starts with three identical digits<sub>7</sub><ref name="digit"/>. * ... is the smallest positive integer ''n'' such that ''n''<sup>''n''</sup> is pandigital<sub>7</sub><ref name="pandigital"/>. * ... is a value for ''n'' such that 1/''n'' is a "nice" fractional Friedman<sub>14</sub><ref name="almostfriedman"/> number: 1/9 = 1<sup>7+10+12</sup>/(6+3) * ... is a (1)-shifted Friedman<sub>7</sub><ref name="friedmanpair"/> number: 9 = 3<sup>2</sup> * ..., as 1<sup>1</sup>+2<sup>3</sup>, is a handsome<sub>7</sub><ref name="handsome"/> number. * ... is the largest digit in base<ref name="base"/> 10. * ... is shaped like the Extended Shidinn letter pronounced like "thw" as in "thwarted". </div> ===10=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive even number ''n'' where ''n''-1 is a Fermat pseudoprime<sub>''n''</sub><ref name="psp"/>. * ... is the smallest positive integer that is not a Harshad<sub>7</sub><ref name="harshad"/> number. * ..., as 1<sup>1</sup>+3<sup>2</sup>, is a handsome<sub>7</sub><ref name="handsome"/> number. * ... is a Narcissistic<sub>7</sub><ref name="narcissistic"/> number. * ... is a disarium<sub>7</sub><ref name="disarium"/> number. * ... is the smallest positive integer value of ''n'' such that the digits<sub>7</sub><ref name="digit"/> of ''n'' are all odd, while the digits<sub>7</sub> of ''n''<sup>2</sup> are all even. * ... is the smallest positive non-palindromic<sub>7</sub><ref name="palindromic"/> integer whose square is palindromic<sub>7</sub>. * ... is the number of digits<sub>7</sub><ref name="digit"/> after the point to be scanned<ref name="constantdigitscanning"/> in order to get all seven digits<sub>7</sub> from π. * ... is the unique positive integer that comes between <math>\sqrt{7\times14}</math> and <math>\frac{7+14}{2}</math>. * ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number. * ... is the number of current members in the Shidinn community administration committee. </div> ===11=== <div style="border:2px solid blue"> * ... is the smallest positive odd prime number that is not palindromic<sub>2</sub><ref name="palindromic"/>. * ... is the smallest Honaker<sub>7</sub><ref name="honaker"/> prime. * ... is a prime factor of the tenth smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... is the smaller prime factor of the fifth smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is a value for ''n'' such that 1/''n'' is a "nice" fractional Friedman<sub>14</sub><ref name="almostfriedman"/> number: 1/11 = 1<sup>3+11</sup>/(6+5) </div> ===12=== <div style="border:2px solid #ff00ff"> * ... is the smallest abundant number. * ... is the number of two-digit<sub>7</sub><ref name="digit"/> prime numbers. * ... is the only non-palindromic<sub>7</sub><ref name="palindromic"/> two-digit<sub>7</sub><ref name="digit"/> number that divides its reversal<sub>7</sub><ref name="reversal"/>. * ... is the only two-digit<sub>7</sub> composite number that has a smaller multiset of prime factors<ref name="technical"/> than its reversal<sub>7</sub> does. (citation needed) * ... is a "nice" (1)-shifted Friedman<sub>7</sub><ref name="friedmanpair"/> number: 12 = 2×6 * ... is the smallest known positive non-unity integer ''n'' such that there exists a five-digit<sub>n</sub><ref name="digit"/> number k=a×n<sup>4</sup>+b×n<sup>3</sup>+c×n<sup>2</sup>+d×n+f satisfying that k-2, k-1, k, k+1 and k+2 have a, b, c, d and f (i. e. its digits) positive factors respectively. More surprisingly, that number is a repdigit<sub>12</sub><ref name="repdigit"/> number. * ... is the smallest true composite number. </div> ===13=== <div style="border:2px solid blue"> * ... is the number of Archimedean solids. * ... is the largest digit<sub>14</sub><ref name="digit"/>. * ... is the third smallest repunit<sub>3</sub><ref name="repunit"/> number. * ... is an RDI<sub>7</sub><ref name="rdi"/> of order 2. * ... is the smallest positive odd Fibonacci number that is not palindromic<sub>2</sub><ref name="palindromic"/>. * ... is a prime factor of the 12th smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... is a prime factor of the 13th smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is the number that represents Devil in western culture. </div> ===14=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive two-digit<sub>14</sub><ref name="digit"/> number. * ... is the smallest positive semiprime that is not a brilliant<sub>7</sub><ref name="brilliant"/> number. * ... is the smallest two-digit<sub>7</sub><ref name="digit"/> "kind<sub>7</sub>"<ref name="a185186"/> number. * ... is the smallest integer ''n'' such that e<sup>''n''</sup> exceeds 7<sup>7</sup>. * ... is the largest known positive non-unity integer ''n'' such that an ''n''-digit<sub>''n''</sub><ref name="digit"/> pandigital<sub>''n''</sub><ref name="pandigital"/> "magic"<sub>''n''</sub><ref name="a144688"/> number exists. * ... is the index of the nasal sibilant in the [[Shidinn alphabet]]. </div> ===15=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive odd composite number that is not a perfect power. * ... is the second smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is the number of two-digit<sub>14</sub><ref name="digit"/> triangular numbers. * ... is the smallest Fermat pseudoprime<sub>14</sub><ref name="psp"/>.<!-- digit period 2 divides 15-1 --> </div> ===16=== <div style="border:2px solid #ff00ff"> * ... is the second smallest positive tesseractic number. * ... is the smallest positive integer with five positive factors. * ... is a repdigit<sub>7</sub><ref name="repdigit"/> number. * ... is a "nice" (2)-shifted Friedman<sub>7</sub><ref name="friedmanpair"/> number: 16 = 4×4 * ... is the second smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. * ... is the smallest positive composite number whose reversal<sub>14</sub><ref name="reversal"/> is prime. </div> ===17=== <div style="border:2px solid blue"> * ... is a Fermat prime. * ... is the smallest prime number that is the concatenation<sub>7</sub><ref name="concatenation"/> of two prime numbers. </div> ===18=== <div style="border:2px solid #ff00ff"> * ... is the only known Canada<sub>7</sub><ref name="canada"/> number. * ... is the smallest two-digit<sub>14</sub><ref name="digit"/> number in the Fibonacci-like sequence starting with 2 and 1. </div> ===19=== <div style="border:2px solid blue"> * ... is the smallest positive odd prime number whose reversal<sub>2</sub><ref name="reversal"/> is composite. </div> ===20=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> is pandigital<sub>7</sub><ref name="pandigital"/>. * ... is the smallest positive non-repdigit<sub>7</sub> integer whose square is repdigit<sub>7</sub><ref name="repdigit"/>. * ... is the smallest positive non-palindromic<sub>7</sub><ref name="palindromic"/> integer whose tesseractic is palindromic<sub>7</sub>. * ... is the integer that caused an "e-mail war" between Shidinn enthusiasts on February 24, 2025. </div> ===21=== <div style="border:2px solid #ff00ff"> * ... is the sum of all the one-digit<sub>7</sub><ref name="digit"/> numbers. It is also the numbers of dots on the dice used in most of the board games. * ... is the third smallest repunit<sub>4</sub><ref name="repunit"/> number. * ... is the smallest positive odd semiprime that is not a brilliant<sub>7</sub><ref name="brilliant"/> number. * ... is the third smallest<sup>[lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>]</sup> positive integer whose tesseractic is a happy<sub>14</sub><ref name="happy"/> number. </div> ===22=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' whose square "ends with the digit<sub>7</sub><ref name="digit"/> it starts with, but is not palindromic<sub>7</sub><ref name="palindromic"/>". * ... has a square root with a seven-digit<sub>7</sub><ref name="digit"/> string of copies of "4" and "5" immediately after the point. </div> ===23=== <div style="border:2px solid blue"> * ... is the smallest positive odd prime number that is not a twin prime. * ... is the smaller prime factor of 2047, the smallest Mersenne composite number. * ... is the smallest two-digit<sub>14</sub><ref name="digit"/> prime number ''n'' such that 210-''n'' is composite. * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> starts in two identical digits<sub>14</sub><ref name="digit"/>. * ... is a prime factor of the seventh smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. </div> ===24=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> ends in three identical digits<sub>7</sub><ref name="digit"/>. * ... is the minimum difference between two distinct positive prime numbers that can be expressed as 8 times a square number plus 27 times a square number. This property of prime numbers was mentioned by a Shidinn enthusiast as an "unfortunate" property. </div> ===25=== <div style="border:2px solid #ff00ff"> * ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number. * ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2. * ... is the smallest Fermat pseudoprime<sub>7</sub><ref name="psp"/>.<!-- digit period 4 divides 25-1 --> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> starts in three identical digits<sub>7</sub><ref name="digit"/> and ends in three identical digits<sub>7</sub>. </div> ===26=== <div style="border:2px solid #ff00ff"> * ... is the median of all two-digit<sub>7</sub><ref name="digit"/> prime numbers. * ... is the smallest positive integer ''n'' whose digit<sub>7</sub><ref name="digit"/> median is an integer that doesn't divide ''n''. </div> ===27=== <div style="border:2px solid #ff00ff"> * ... is the second smallest composite Smith<sub>7</sub><ref name="smith"/> number. * ... is the only known two-digit<sub>7</sub> composite Smith<sub>7</sub><ref name="smith"/> number. * ... appears in an example of Anomalous Cancellation<ref name="anomalouscancellation"/> of digits<sub>14</sub>: 27/189=1/7 * ... is the smallest non-unity positive integer ''n'' whose set of prime divisors<ref name="technical"/> is a proper subset of its set of digits<sub>7</sub><ref name="digit"/>. <!-- One-digit numbers don't qualify. If it's a two-digit number, then it must be a prime or prime power. The primes don't qualify because they're too big. 8 is a repdigit. 9 doesn't have a 3 as a digit. 16 is also repdigit. 25 doesn't have 5 as a digit. So 27 is the smallest. --> </div> ===28=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive triangular number whose first digit<sub>14</sub><ref name="digit"/> is larger than its last digit<sub>14</sub>. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. </div> ===29=== <div style="border:2px solid blue"> * ... is the smallest positive odd prime number whose reversal<sub>14</sub><ref name="reversal"/> is composite. * ... is the number of distinct 3D pentominoes, if mirror reflections are considered different. Note that xp0_1$71 is symmetric. * ... is the smaller prime factor of the seventh smallest repunit<sub>7</sub><ref name="repunit"/> number. The unicode character whose ID is the seventh smallest repunit<sub>7</sub> number can be written in Shidinn as Ɐko. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. * ... is the second smallest two-digit<sub>14</sub><ref name="digit"/> number in the Fibonacci-like sequence starting with 2 and 1. * ... is a repfigit<sub>14</sub><ref name="repfigit"/> number. </div> ===30=== <div style="border:2px solid #ff00ff"> * ... is a repdigit<sub>14</sub><ref name="repdigit"/> number. * ... is the number of two-digit<sub>7</sub><ref name="digit"/> composite numbers. * ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number. </div> ===31=== <div style="border:2px solid blue"> * ... is a Mersenne prime. * ... is the smallest positive odd prime number whose reversal<sub>7</sub><ref name="reversal"/> is composite. * ... is the unique two-digit<sub>7</sub><ref name="digit"/> prime number whose reversal<sub>7</sub><ref name="reversal"/> is composite. * ... is the smallest prime number that is the concatenation<sub>14</sub><ref name="concatenation"/> of two prime numbers. * ... is the "home prime"<sub>14</sub><ref name="homeprime"/> reached from 6. * ... is the smallest positive integer whose tesseractic has 8 digits<sub>7</sub><ref name="digit"/>. * ... is the smallest positive integer whose tesseractic is pandigital<sub>7</sub><ref name="pandigital"/>. * ... is the third smallest repunit<sub>5</sub><ref name="repunit"/> number. </div> ===32=== <div style="border:2px solid #ff00ff"> * ... is a repdigit<sub>7</sub><ref name="repdigit"/> number. * ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number. * ... is the second smallest positive hyperhypercube number. </div> ===33=== <div style="border:2px solid #ff00ff"> </div> ===34=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive semiprime that is not a brilliant<sub>14</sub><ref name="brilliant"/> number. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... is the smallest known number in a Friedman<sub>14</sub> loop<ref name="friedmanpair"/>: :: 2<sup>6</sup>=64 :: 8<sup>4</sup>=4096 :: 6×(12×8-1)=570 :: 2×12+10=34 </div> ===35=== <div style="border:2px solid #ff00ff"> * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. * ... is in a Friedman<sub>14</sub> loop<ref name="friedmanpair"/>: :: 7<sup>3</sup>=343 :: (1+10)×7=77 :: 5×7=35 :: 7<sup>2</sup>=49 </div> ===36=== <div style="border:2px solid #ff00ff"> * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. * ... is a "nice" (1)-shifted Friedman<sub>7</sub><ref name="friedmanpair"/> number: 36 = 6<sup>2</sup> </div> ===37=== <div style="border:2px solid blue"> * ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2. * ... is a prime factor of the ninth smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... is a prime factor of the twelfth smallest repunit<sub>14</sub><ref name="repunit"/> number. </div> ===38=== <div style="border:2px solid #ff00ff"> * ... is the number of two-digit<sub>14</sub><ref name="digit"/> prime numbers. </div> ===39=== <div style="border:2px solid #ff00ff"> * ... is the smallest non-palindromic<sub>14</sub><ref name="palindromic"/> two-digit<sub>14</sub><ref name="digit"/> number that divides its reversal<sub>14</sub><ref name="reversal"/>. </div> ===40=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that the set {15<sup>k</sup>|k∈N} has no ''n''-digit<sub>14</sub><ref name="digit"/> member. * ... is in a Friedman<sub>14</sub> pair<ref name="friedmanpair"/>: :: 12<sup>2</sup>=144 :: 4×10=40 </div> ===41=== <div style="border:2px solid blue"> * ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> prime numbers. * ... is one of four possible values of a two-digit<sub>14</sub><ref name="digit"/> prime number ''n'' such that 210-''n'' is composite. * ... is a prime factor of the eighth smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is a value for ''n'' such that 1/''n'' is a "nice" fractional Friedman<sub>14</sub><ref name="almostfriedman"/> number: 1/41 = 0 + 4/(10 + 181 - 9×3×1) * ... is the vertical stroke in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===42=== <div style="border:2px solid #ff00ff"> * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. * ... is the number of U. S. states in the fictional [[希顶世界线|Shidinn timeline]]. * ... is the number that was been thought as the truth of the universe. * ... is the number of years between Jay Chou's date of birth and the creation of this wiki. Jay Chou and Shidinn Wiki have the same birthday. (This entry was added by Translated ORK, making it questionable.) * ... is the word for "two" (Unicode decimal 20108) in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===43=== <div style="border:2px solid blue"> * ... is the third smallest repunit<sub>6</sub><ref name="repunit"/> number. * ... is the first two digits<sub>14</sub><ref name="digit"/> of pi, i. e. floor(14×π). * ... is the largest prime factor of the sixth smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its factorial, the resulting number is square. </div> ===44=== <div style="border:2px solid #ff00ff"> </div> ===45=== <div style="border:2px solid #ff00ff"> * ... is the number of letters in the [[Shidinn alphabet]]. * ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number. * ... is the third smallest<sup>[lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>]</sup> positive integer whose tesseractic is a happy<sub>7</sub><ref name="happy"/> number. </div> ===46=== <div style="border:2px solid #ff00ff"> * ... is the smallest Canada<sub>14</sub><ref name="canada"/> number. * ... is equal to the rebasing<sub>7→10</sub><ref name="rebasing"/> of its own reversal<sub>7</sub><ref name="reversal"/>. It is also the arithmetic square root of another integer with the same property. * ... is the word for "prostrate" (Unicode decimal 20239) in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===47=== <div style="border:2px solid blue"> * ... is the largest two-digit<sub>7</sub><ref name="digit"/> prime number. * ... is the largest positive integer such that every number resulting from removing some (or none) of its trailing digits<sub>2</sub> is either 0, 1, or a prime number. (OEIS A165802) This fact is mentioned on the website given below. * ... is the [[平原素数系统|representative prime number]] of [[User:Rachel1211]]. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 4. * ... is the smallest positive integer whose tesseractic has the last 3 digits<sub>7</sub><ref name="digit"/> the same as the three digits<sub>7</sub> before that. * ... is a value for ''n'' such that the tesseractic of ''n'' can be written as the reversal<sub>7</sub><ref name="reversal"/> of ''n'' concatenated<sub>7</sub><ref name="concatenation"/> with two identical three-digit<sub>7</sub> strings. * ... is featured on [http://www.zhihu.com/question/12695389890 this website]. You can submit entries there. </div> ===48=== <div style="border:2px solid #ff00ff"> * ... is the largest two-digit<sub>7</sub><ref name="digit"/> number. * ... is the word for "kindness" (Unicode decimal 24681) in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===49=== <div style="border:2px solid #ff00ff"> * ... is the smallest three-digit<sub>7</sub><ref name="digit"/> number. * ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> composite numbers. * ... is the smallest positive composite number whose prime indices are all composite. </div> ===50=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive palindromic<sub>7</sub><ref name="palindromic"/> number that is not repdigit<sub>7</sub><ref name="repdigit"/>. * ... is the smallest Cyclops<sub>7</sub><ref name="cyclops"/> number. </div> ===51=== <div style="border:2px solid #ff00ff"> * ... is the smallest Cyclops<sub>7</sub><ref name="cyclops"/> number that is not palindromic<sub>7</sub><ref name="palindromic"/>. * ... is the smallest positive odd semiprime that is not a brilliant<sub>14</sub><ref name="brilliant"/> number. </div> ===52=== <div style="border:2px solid #ff00ff"> * ... is the word for "offer" (Unicode decimal 29486) in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===53=== <div style="border:2px solid blue"> * ... is the smallest three-digit<sub>7</sub><ref name="digit"/> prime number. * ... is the number of three-digit<sub>7</sub><ref name="digit"/> prime numbers. * ... is the smallest positive prime number that is not alternating<sub>7</sub><ref name="alternating"/>. * ... is the smallest positive prime number with digit<sub>7</sub> median 1. * ... is the smallest Cyclops<sub>7</sub><ref name="cyclops"/> prime number. * ... is the word for "heart" (Unicode decimal 24515) in [[Shidinn]] [[聊天字母|chat alphabet]]. </div> ===54=== <div style="border:2px solid #ff00ff"> * ... is the smallest three-digit<sub>7</sub><ref name="digit"/> abundant number. * ... is the smallest Cyclops<sub>7</sub><ref name="cyclops"/> number ''n'' such that the ''n''th prime number is also a Cyclops<sub>7</sub> number. </div> ===55=== <div style="border:2px solid #ff00ff"> * ... is the second smallest positive integer that is both square pyramidal and triangular, as mentioned by a Shidinn enthusiast. </div> ===56=== <div style="border:2px solid #ff00ff"> * ... is the largest two-digit<sub>7ans</sub><ref name="ans"/> number. * ... is the number of [[Chinese character sounds of Shidinn|Hanzi]] characters in the [[Firefly]] poem. </div> ===57=== <div style="border:2px solid #ff00ff"> * ... is the third smallest repunit<sub>7</sub><ref name="repunit"/> number. * ... is the smallest three-digit<sub>7ans</sub><ref name="ans"/> number. * ... is the smallest positive odd composite number whose digits<sub>7</sub><ref name="digit"/> are all odd. * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its square, the resulting number is square. * ... is the number of distinct symbols in the standard "Spot it" pack, with 8 symbols on each card. (See [[#73|<span style="color:green;">73</span>]]) </div> ===58=== <div style="border:2px solid #ff00ff"> </div> ===59=== <div style="border:2px solid blue"> * ... is the smallest three-digit<sub>7</sub><ref name="digit"/> twin prime. * ... is the smallest positive prime number with digit<sub>7</sub> mode 1. * ... is a prime factor of the sixth smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. * ... is the smallest prime number that can be expressed as 8 times a square number plus 27 times a square number. This property of prime numbers was mentioned by a Shidinn enthusiast as an "unfortunate" property. </div> ===60=== <div style="border:2px solid #ff00ff"> </div> ===61=== <div style="border:2px solid blue"> * ... is a prime factor of the sixth smallest repunit<sub>14</sub><ref name="repunit"/> number. </div> ===62=== <div style="border:2px solid #ff00ff"> </div> ===63=== <div style="border:2px solid #ff00ff"> </div> ===64=== <div style="border:2px solid #ff00ff"> </div> ===65=== <div style="border:2px solid #ff00ff"> * ..., as [http://mathworld.wolfram.com/ExpandedNotation.html 4×14+9], is a Cyclic<sub>14</sub> number<ref name="frp"/>, according to Wolfram Mathworld. </div> ===66=== <div style="border:2px solid #ff00ff"> * ... is the third smallest Smarandache<sub>7</sub><ref name="smarandache"/> number. * ... is the third smallest positive triangular number whose digits<sub>14</sub><ref name="digit"/> are all semiprime. </div> ===67=== <div style="border:2px solid blue"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> is the concatenation<sub>14</sub><ref name="concatenation"/> of ''n'' and another integer. * ... is the second smallest positive integer whose square is a Cyclops<sub>7</sub><ref name="cyclops"/> number. * ... is one of four possible values of a two-digit<sub>14</sub><ref name="digit"/> prime number ''n'' such that 210-''n'' is composite. * ... is a prime factor of the eleventh smallest repunit<sub>14</sub><ref name="repunit"/> number. </div> ===68=== <div style="border:2px solid #ff00ff"> </div> ===69=== <div style="border:2px solid #ff00ff"> </div> ===70=== <div style="border:2px solid #ff00ff"> * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. </div> ===71=== <div style="border:2px solid blue"> * ... is the largest known positive integer whose square can be written as one plus the factorial of another positive integer. * ... is the smallest positive palindromic<sub>7</sub><ref name="palindromic"/> prime number that is not repdigit<sub>7</sub><ref name="repdigit"/>. * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... is a prime factor of the tenth smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is featured on [http://www.zhihu.com/question/14793120356 this website]. You can submit entries there. </div> ===72=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer that is not a perfect power but can be written as the product of perfect powers. * ... is the third smallest positive integer whose square is a Cyclops<sub>7</sub><ref name="cyclops"/> number. </div> ===73=== <div style="border:2px solid blue"> * ... is the third smallest repunit<sub>8</sub><ref name="repunit"/> number. * ... is the smallest positive twin prime number such that none of the next three prime numbers is twin prime. * ... is the third smallest positive integer that is both palindromic<sub>2</sub><ref name="palindromic"/> and palindromic<sub>b3<ref name="balancedternary"/></sub>. * ... is the second smallest positive integer that is the sum of three different positive cubic numbers. * ... is the sum of the cubes of the three smallest positive palindromic<sub>3</sub><ref name="palindromic"/> numbers. * ... is the sum of the aliquot parts<ref name="technical"/> of the smallest three-digit<sub>7</sub><ref name="digit"/> number not containing a digit<sub>7</sub> "1". * ... is the smallest positive prime number with digit<sub>7</sub> mode 3. * ... is the smallest non-palindromic<sub>7</sub><ref name="palindromic"/> positive prime number that ends with two identical digits<sub>7</sub><ref name="digit"/>. * ... is the smallest positive integer ''n'' that is equal to the result of removing the digit<sub>7</sub> "0" from the ''n''th positive prime number. * ... is a prime factor of the seventh smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. * ... is the number of cards in the [[Seven elements]] poker game. The pack has 7 suits of 10 cards each, along with three extra cards (INF, 7UT and blank). * ... is the theoretical number of distinct symbols in "Spot it" variant, with 9 symbols (instead of 8) on each card. * ... is a number worshipped in Shidinn culture. * ... is featured on [http://www.zhihu.com/question/8988346680 this website]. You can submit entries there. </div> ===74=== <div style="border:2px solid #ff00ff"> </div> ===75=== <div style="border:2px solid #ff00ff"> </div> ===76=== <div style="border:2px solid #ff00ff"> * ... is the sum of the first three Smarandache<sub>7</sub><ref name="smarandache"/> numbers. </div> ===77=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 15<sup>n</sup> has (''n''+3) digits<sub>14</sub><ref name="digit"/>. </div> ===78=== <div style="border:2px solid #ff00ff"> * ... is the second smallest Canada<sub>14</sub><ref name="canada"/> number. <!-- larger ones include 1945, 16837, 27169, 29749 --> </div> ===79=== <div style="border:2px solid blue"> </div> ===80=== <div style="border:2px solid #ff00ff"> * ... , as 3<sup>4</sup>-1, is a Friedman<sub>7</sub><ref name="friedman"/> number. </div> ===81=== <div style="border:2px solid #ff00ff"> * ... is the third smallest positive tesseractic number. * ... is in the username of [[User:DGCK81LNN]]. </div> ===82=== <div style="border:2px solid #ff00ff"> * ... has a square root with a string of eleven even digits<sub>7</sub><ref name="digit"/>immediately after the point. * ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number. </div> ===83=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>7</sub> median 4. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 9. </div> ===84=== <div style="border:2px solid #ff00ff"> </div> ===85=== <div style="border:2px solid #ff00ff"> * ... is the largest known index of a square pyramidal number that is also triangular. Its index in the triangular sequence is 645. * ... is the smallest positive palindromic<sub>7</sub><ref name="palindromic"/> semiprime that is not repdigit<sub>7</sub><ref name="repdigit"/>. * ... is the prime index of the "home prime"<sub>14</sub><ref name="homeprime"/> reached from 4. * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its cube, the resulting number is square. </div> ===86=== <div style="border:2px solid #ff00ff"> </div> ===87=== <div style="border:2px solid #ff00ff"> </div> ===88=== <div style="border:2px solid #ff00ff"> </div> ===89=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>7</sub> mode 5. * ... is one of four possible values of a two-digit<sub>14</sub><ref name="digit"/> prime number ''n'' such that 210-''n'' is composite. * ... is the total number of letters in the [[Shidinn alphabet]] and the Extended Shidinn alphabet, including the "number zero" letter. </div> ===90=== <div style="border:2px solid #ff00ff"> </div> ===91=== <div style="border:2px solid #ff00ff"> * ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> numbers. * ... is the third smallest repunit<sub>9</sub><ref name="repunit"/> number. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... is the third smallest positive integer that is both square pyramidal and triangular, as mentioned by a Shidinn enthusiast. </div> ===92=== <div style="border:2px solid #ff00ff"> </div> ===93=== <div style="border:2px solid #ff00ff"> </div> ===94=== <div style="border:2px solid #ff00ff"> </div> ===95=== <div style="border:2px solid #ff00ff"> </div> ===96=== <div style="border:2px solid #ff00ff"> </div> ===97=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>7</sub> median 6. * ... is the smallest positive prime number with digit<sub>7</sub> mode 6. * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its square, the resulting number is square. * ... is the last prime number that 10 ≤ x ≤ 99. </div> ===98=== <div style="border:2px solid #ff00ff"> </div> ===99=== <div style="border:2px solid #ff00ff"> * ... is the median of all two-digit<sub>14</sub><ref name="digit"/> prime numbers. </div> ===100=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive Cyclops<sub>7</sub><ref name="cyclops"/> square number. * ... is the smallest 2-digit<sub>100</sub> number. </div> ===101=== <div style="border:2px solid blue"> * ... is the second smallest Cyclops<sub>7</sub><ref name="cyclops"/> prime number. * ... is a prime factor of the tenth smallest repunit<sub>14</sub><ref name="repunit"/> number. </div> ===102=== <div style="border:2px solid #ff00ff"> </div> ===103=== <div style="border:2px solid blue"> * ... is the third smallest Cyclops<sub>7</sub><ref name="cyclops"/> prime number. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 6. </div> ===104=== <div style="border:2px solid #ff00ff"> </div> ===105=== <div style="border:2px solid #ff00ff"> </div> ===106=== <div style="border:2px solid #ff00ff"> </div> ===107=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>7</sub> mode 2. * ... is the sum of all the two-digit<sub>7</sub> "non-twin" prime numbers. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 8. </div> ===108=== <div style="border:2px solid #ff00ff"> </div> ===109=== <div style="border:2px solid blue"> * ... is a prime factor of the 13th smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. </div> ===110=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> is pandigital<sub>14</sub><ref name="pandigital"/>. </div> ===111=== <div style="border:2px solid #ff00ff"> </div> ===112=== <div style="border:2px solid #ff00ff"> </div> ===113=== <div style="border:2px solid blue"> * ... is a prime factor of the 14th smallest repunit<sub>7</sub><ref name="repunit"/> number. </div> ===114=== <div style="border:2px solid #ff00ff"> * ... is the number that is CURRENTLY thought as the truth of the universe. </div> ===115=== <div style="border:2px solid #ff00ff"> </div> ===116=== <div style="border:2px solid #ff00ff"> </div> ===117=== <div style="border:2px solid #ff00ff"> </div> ===118=== <div style="border:2px solid #ff00ff"> </div> ===119=== <div style="border:2px solid #ff00ff"> * ... is the smallest brilliant<sub>7</sub><ref name="brilliant"/> number with four distinct digits<sub>7</sub> in its set of prime factors. (citation needed) </div> ===120=== <div style="border:2px solid #ff00ff"> </div> ===121=== <div style="border:2px solid #ff00ff"> </div> ===122=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> starts with two identical digits<sub>14</sub><ref name="digit"/> followed immediately by two identical digits<sub>14</sub>. </div> ===123=== <div style="border:2px solid #ff00ff"> </div> ===124=== <div style="border:2px solid #ff00ff"> </div> ===125=== <div style="border:2px solid #ff00ff"> </div> ===126=== <div style="border:2px solid #ff00ff"> </div> ===127=== <div style="border:2px solid blue"> * ... is a Mersenne prime. * ... is the smallest Mersenne prime that is "emirp<sub>7</sub>"<ref name="emirp"/>. * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. * ... is a number worshipped in Shidinn culture.<sup>[lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>]</sup> </div> ===128=== <div style="border:2px solid #ff00ff"> </div> ===129=== <div style="border:2px solid #ff00ff"> </div> ===130=== <div style="border:2px solid #ff00ff"> </div> ===131=== <div style="border:2px solid blue"> </div> ===132=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that the ''n''th Fibonacci number is pandigital<sub>14</sub><ref name="pandigital"/>.<sup>[citation needed]</sup> </div> ===133=== <div style="border:2px solid #ff00ff"> </div> ===134=== <div style="border:2px solid #ff00ff"> </div> ===135=== <div style="border:2px solid #ff00ff"> </div> ===136=== <div style="border:2px solid #ff00ff"> * ... is the second smallest triangular number whose digits<sub>7</sub><ref name="digit"/> are all prime. The smallest is 3. * ... is the smallest positive triangular number containing an odd semiprime digit<sub>14</sub> and an even semiprime digit<sub>14</sub>. * ... is the smallest three-digit<sub>10</sub> triangular number such that every number resulting from removing some (or none) of its leading digits<sub>10</sub> is either 0 or a triangular number. (observed by [[User:List of deleted users]])<br>This property is preserved in tetradecimal as well, except that it is now a two-digit<sub>14</sub> number. * ... is the index (in [[荆哲歌单|Infinite Song List]]) of the song whose original title is a result from spelling the word for [[遗迹(希顶世界线)|"relics"]] backwards in the Japanese syllabary. * ... is the number of standard [[希顶麻将|"Mahjong"]] tiles, excluding the seasons and plants. </div> ===137=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 10. </div> ===138=== <div style="border:2px solid #ff00ff"> </div> ===139=== <div style="border:2px solid blue"> </div> ===140=== <div style="border:2px solid #ff00ff"> </div> ===141=== <div style="border:2px solid #ff00ff"> </div> ===142=== <div style="border:2px solid #ff00ff"> </div> ===143=== <div style="border:2px solid #ff00ff"> </div> ===144=== <div style="border:2px solid #ff00ff"> * ... is the smallest xenodromic<sub>7</sub><ref name="xenodromic"/> three-digit<sub>7</sub> square number. * ... is a square number such that moving the first digit<sub>7</sub> to the last gives a larger square number. </div> ===145=== <div style="border:2px solid #ff00ff"> </div> ===146=== <div style="border:2px solid #ff00ff"> </div> ===147=== <div style="border:2px solid #ff00ff"> </div> ===148=== <div style="border:2px solid #ff00ff"> </div> ===149=== <div style="border:2px solid blue"> * ... is the fourth smallest Cyclops<sub>7</sub><ref name="cyclops"/> prime number. * ... is the smallest prime number whose digits<sub>14</sub><ref name="digit"/> are all composite. </div> ===150=== <div style="border:2px solid #ff00ff"> </div> ===151=== <div style="border:2px solid blue"> </div> ===152=== <div style="border:2px solid #ff00ff"> </div> ===153=== <div style="border:2px solid #ff00ff"> </div> ===154=== <div style="border:2px solid #ff00ff"> * ... is the smallest sphenic<ref name="sphenic"/> number whose prime factors all end in an even digit<sub>7</sub>. </div> ===155=== <div style="border:2px solid #ff00ff"> </div> ===156=== <div style="border:2px solid #ff00ff"> </div> ===157=== <div style="border:2px solid blue"> * ... is a prime factor of the 13th smallest repunit<sub>14</sub><ref name="repunit"/> number. </div> ===158=== <div style="border:2px solid #ff00ff"> </div> ===159=== <div style="border:2px solid #ff00ff"> </div> ===160=== <div style="border:2px solid #ff00ff"> </div> ===161=== <div style="border:2px solid #ff00ff"> </div> ===162=== <div style="border:2px solid #ff00ff"> </div> ===163=== <div style="border:2px solid blue"> </div> ===164=== <div style="border:2px solid #ff00ff"> </div> ===165=== <div style="border:2px solid #ff00ff"> </div> ===166=== <div style="border:2px solid #ff00ff"> </div> ===167=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 12. </div> ===168=== <div style="border:2px solid #ff00ff"> * ... has the property that if each digit<sub>14</sub><ref name="digit"/> is replaced by its square, the resulting number is a triangular number. </div> ===169=== <div style="border:2px solid #ff00ff"> </div> ===170=== <div style="border:2px solid #ff00ff"> </div> ===171=== <div style="border:2px solid #ff00ff"> * ... is the third smallest triangular number whose digits<sub>7</sub><ref name="digit"/> are all prime. * ... is the fourth smallest positive repdigit<sub>7</sub><ref name="repdigit"/> triangular number. * ... is the smallest positive triangular number whose first digit<sub>14</sub><ref name="digit"/> is larger than its last non-zero digit<sub>14</sub>. * ... is the sum of all positive factors of the smallest three-digit<sub>7</sub><ref name="digit"/> number not containing a digit<sub>7</sub> "1". </div> ===172=== <div style="border:2px solid #ff00ff"> </div> ===173=== <div style="border:2px solid blue"> </div> ===174=== <div style="border:2px solid #ff00ff"> </div> ===175=== <div style="border:2px solid #ff00ff"> </div> ===176=== <div style="border:2px solid #ff00ff"> </div> ===177=== <div style="border:2px solid #ff00ff"> </div> ===178=== <div style="border:2px solid #ff00ff"> </div> ===179=== <div style="border:2px solid blue"> * ... is the smallest positive prime number with digit<sub>7</sub><ref name="digit"/> mode 4. </div> ===180=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that ''n''<sup>2</sup> starts in two identical digits<sub>14</sub><ref name="digit"/> and ends in two identical digits<sub>14</sub>. </div> ===181=== <div style="border:2px solid blue"> * ... is a prime factor of the 12th smallest repunit<sub>7</sub><ref name="repunit"/> number. </div> ===182=== <div style="border:2px solid #ff00ff"> * ... is the number of Shidinn letters in the [[Firefly]] poem. </div> ===183=== <div style="border:2px solid #ff00ff"> </div> ===184=== <div style="border:2px solid #ff00ff"> </div> ===185=== <div style="border:2px solid #ff00ff"> </div> ===186=== <div style="border:2px solid #ff00ff"> </div> ===187=== <div style="border:2px solid #ff00ff"> </div> ===188=== <div style="border:2px solid #ff00ff"> </div> ===189=== <div style="border:2px solid #ff00ff"> </div> ===190=== <div style="border:2px solid #ff00ff"> </div> ===191=== <div style="border:2px solid blue"> * ... is a prime factor of the tenth smallest repunit<sub>7</sub><ref name="repunit"/> number. </div> ===192=== <div style="border:2px solid #ff00ff"> </div> ===193=== <div style="border:2px solid blue"> * ... is the largest two-digit<sub>14</sub><ref name="digit"/> prime number. * ... is a prime factor of the twelfth smallest Smarandache<sub>14</sub><ref name="smarandache"/> number. </div> ===194=== <div style="border:2px solid #ff00ff"> </div> ===195=== <div style="border:2px solid #ff00ff"> * ... is the largest two-digit<sub>14</sub><ref name="digit"/> number. </div> ===196=== <div style="border:2px solid #ff00ff"> * ... is the smallest three-digit<sub>14</sub><ref name="digit"/> number. </div> ===197=== <div style="border:2px solid blue"> * ... is the smallest three-digit<sub>14</sub><ref name="digit"/> prime number. * ... is the smallest positive palindromic<sub>14</sub><ref name="palindromic"/> number that is not repdigit<sub>14</sub><ref name="repdigit"/>. * ... is the smallest positive palindromic<sub>14</sub><ref name="palindromic"/> prime number that is not repdigit<sub>14</sub><ref name="repdigit"/>. * ... is the smallest Cyclops<sub>14</sub><ref name="cyclops"/> number. * ... is the smallest Cyclops<sub>14</sub><ref name="cyclops"/> prime number. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> median 1. * ... is the smallest positive prime number with digit<sub>14</sub><ref name="digit"/> mode 1. </div> ===198=== <div style="border:2px solid #ff00ff"> * ... is the smallest Cyclops<sub>14</sub><ref name="cyclops"/> number that is not palindromic<sub>14</sub><ref name="palindromic"/>. * ... is the smallest composite Cyclops<sub>14</sub><ref name="cyclops"/> number. </div> ===199=== <div style="border:2px solid blue"> </div> ===200=== <div style="border:2px solid #ff00ff"> </div> ===201=== <div style="border:2px solid #ff00ff"> * ... is the smallest three-digit<sub>14</sub><ref name="digit"/> squarefree<ref name="squarefree"/> composite number. </div> ===202=== <div style="border:2px solid #ff00ff"> </div> ===203=== <div style="border:2px solid #ff00ff"> </div> ===204=== <div style="border:2px solid #ff00ff"> </div> ===205=== <div style="border:2px solid #ff00ff"> </div> ===206=== <div style="border:2px solid #ff00ff"> </div> ===207=== <div style="border:2px solid #ff00ff"> </div> ===208=== <div style="border:2px solid #ff00ff"> </div> ===209=== <div style="border:2px solid #ff00ff"> </div> ===210=== <div style="border:2px solid #ff00ff"> </div> ===211=== <div style="border:2px solid blue"> * ... is the third smallest repunit<sub>14</sub><ref name="repunit"/> number. * ... is the smallest repunit<sub>14</sub><ref name="repunit"/> prime number. </div> ===212=== <div style="border:2px solid #ff00ff"> </div> ===213=== <div style="border:2px solid #ff00ff"> </div> ===214=== <div style="border:2px solid #ff00ff"> </div> ===215=== <div style="border:2px solid #ff00ff"> </div> ===216=== <div style="border:2px solid #ff00ff"> </div> ===217=== <div style="border:2px solid #ff00ff"> </div> ===218=== <div style="border:2px solid #ff00ff"> </div> ===219=== <div style="border:2px solid #ff00ff"> </div> ===220=== <div style="border:2px solid #ff00ff"> </div> ===221=== <div style="border:2px solid #ff00ff"> </div> ===222=== <div style="border:2px solid #ff00ff"> </div> ===223=== <div style="border:2px solid blue"> </div> ===224=== <div style="border:2px solid #ff00ff"> </div> ===225=== <div style="border:2px solid #ff00ff"> * ... is the second smallest three-digit<sub>14</sub><ref name="digit"/> square number. </div> ===226=== <div style="border:2px solid #ff00ff"> </div> ===227=== <div style="border:2px solid blue"> * ... is the third smallest Smarandache<sub>14</sub><ref name="smarandache"/> number, as well as the smallest Smarandache<sub>14</sub> prime number. * ... is the second smallest prime number that can be expressed as 8 times a square number plus 27 times a square number. This property of prime numbers was mentioned by a Shidinn enthusiast as an "unfortunate" property. </div> ===228=== <div style="border:2px solid #ff00ff"> </div> ===229=== <div style="border:2px solid blue"> </div> ===230=== <div style="border:2px solid #ff00ff"> </div> ===231=== <div style="border:2px solid #ff00ff"> </div> ===232=== <div style="border:2px solid #ff00ff"> </div> ===233=== <div style="border:2px solid blue"> </div> ===234=== <div style="border:2px solid #ff00ff"> </div> ===235=== <div style="border:2px solid #ff00ff"> </div> ===236=== <div style="border:2px solid #ff00ff"> </div> ===237=== <div style="border:2px solid #ff00ff"> </div> ===238=== <div style="border:2px solid #ff00ff"> </div> ===239=== <div style="border:2px solid blue"> </div> ===240=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> starts in two identical digits<sub>14</sub><ref name="digit"/> and ends in two identical digits<sub>14</sub>. </div> ===241=== <div style="border:2px solid blue"> </div> ===242=== <div style="border:2px solid #ff00ff"> </div> ===243=== <div style="border:2px solid #ff00ff"> </div> ===244=== <div style="border:2px solid #ff00ff"> </div> ===245=== <div style="border:2px solid #ff00ff"> </div> ===246=== <div style="border:2px solid #ff00ff"> </div> ===247=== <div style="border:2px solid #ff00ff"> </div> ===248=== <div style="border:2px solid #ff00ff"> </div> ===249=== <div style="border:2px solid #ff00ff"> </div> ===250=== <div style="border:2px solid #ff00ff"> </div> ===251=== <div style="border:2px solid blue"> </div> ===252=== <div style="border:2px solid #ff00ff"> </div> ===253=== <div style="border:2px solid #ff00ff"> * ... is the smallest positive palindromic<sub>14</sub><ref name="palindromic"/> triangular number that is not repdigit<sub>14</sub><ref name="repdigit"/>. </div> ===254=== <div style="border:2px solid #ff00ff"> </div> ===255=== <div style="border:2px solid #ff00ff"> * ... is the smallest sphenic<ref name="sphenic"/> number whose prime factors all end in an odd digit<sub>7</sub>. </div> ===256=== <div style="border:2px solid #ff00ff"> </div> ===257=== <div style="border:2px solid blue"> * ... has the property that if each digit<sub>7</sub><ref name="digit"/> is replaced by its square, the resulting number is square. </div> ===258=== <div style="border:2px solid #ff00ff"> </div> ===259=== <div style="border:2px solid #ff00ff"> </div> ===260=== <div style="border:2px solid #ff00ff"> </div> ===261=== <div style="border:2px solid #ff00ff"> </div> ===262=== <div style="border:2px solid #ff00ff"> </div> ===263=== <div style="border:2px solid blue"> </div> ===264=== <div style="border:2px solid #ff00ff"> </div> ===265=== <div style="border:2px solid #ff00ff"> </div> ===266=== <div style="border:2px solid #ff00ff"> </div> ===267=== <div style="border:2px solid #ff00ff"> </div> ===268=== <div style="border:2px solid #ff00ff"> </div> ===269=== <div style="border:2px solid blue"> </div> ===270=== <div style="border:2px solid #ff00ff"> </div> ===271=== <div style="border:2px solid blue"> </div> ===272=== <div style="border:2px solid #ff00ff"> </div> ===273=== <div style="border:2px solid #ff00ff"> </div> ===274=== <div style="border:2px solid #ff00ff"> </div> ===275=== <div style="border:2px solid #ff00ff"> </div> ===276=== <div style="border:2px solid #ff00ff"> </div> ===277=== <div style="border:2px solid blue"> </div> ===278=== <div style="border:2px solid #ff00ff"> </div> ===279=== <div style="border:2px solid #ff00ff"> </div> ===280=== <div style="border:2px solid #ff00ff"> </div> ===281=== <div style="border:2px solid blue"> </div> ===282=== <div style="border:2px solid #ff00ff"> </div> ===283=== <div style="border:2px solid blue"> </div> ===284=== <div style="border:2px solid #ff00ff"> </div> ===285=== <div style="border:2px solid #ff00ff"> </div> ===286=== <div style="border:2px solid #ff00ff"> </div> ===287=== <div style="border:2px solid #ff00ff"> </div> ===288=== <div style="border:2px solid #ff00ff"> </div> ===289=== <div style="border:2px solid #ff00ff"> </div> ===290=== <div style="border:2px solid #ff00ff"> </div> ===291=== <div style="border:2px solid #ff00ff"> </div> ===292=== <div style="border:2px solid #ff00ff"> </div> ===293=== <div style="border:2px solid blue"> </div> ===294=== <div style="border:2px solid #ff00ff"> </div> ===295=== <div style="border:2px solid #ff00ff"> </div> ===296=== <div style="border:2px solid #ff00ff"> </div> ===297=== <div style="border:2px solid #ff00ff"> </div> ===298=== <div style="border:2px solid #ff00ff"> </div> ===299=== <div style="border:2px solid #ff00ff"> </div> ===300=== <div style="border:2px solid #ff00ff"> </div> ==See also== ==Notes== <references group="note"> <ref name="za14">In Zbalermorna Abjad numerical system, ignoring the "li" and the "ju'u pavo lo'o".</ref> </references> ==References== <references><ref name="base">'''[http://mathworld.wolfram.com/Base.html Base] on Wolfram Mathwold'''<sup>(1)</sup></ref><ref name="digit">[http://mathworld.wolfram.com/Digit.html Digit] on Wolfram Mathworld</ref> <ref name="constantdigitscanning">[http://mathworld.wolfram.com/ConstantDigitScanning.html Constant digit scanning] on Wolfram Mathworld</ref> <ref name="concatenation">[http://mathworld.wolfram.com/Concatenation.html Concatenation] on Wolfram Mathworld</ref> <ref name="reversal">[http://mathworld.wolfram.com/Reversal.html Reversal] on Wolfram Mathworld</ref> <ref name="rebasing">[http://oeis.org/wiki/Rebasing_notation Rebasing] on OEIS Wiki</ref> <ref name="palindromic">[http://mathworld.wolfram.com/PalindromicNumber.html Palindromic] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/palindromic_number/ Palindromic] on NUMBERSAPLENTY</ref> <ref name="alternating">[http://www.numbersaplenty.com/set/alternating_number/ Alternating number] on NUMBERSAPLENTY<!--Alternating odd and even digits--></ref> <ref name="cyclops">[http://oeis.org/A134808 Cyclops number] on OEIS</ref> <ref name="repdigit">[http://mathworld.wolfram.com/Repdigit.html Repdigit] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/repdigit/ Repdigit] on NUMBERSAPLENTY</ref> <ref name="repunit">[http://mathworld.wolfram.com/Repunit.html Repunit] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/repunit/ Repunit] on NUMBERSAPLENTY</ref> <ref name="pandigital">[http://mathworld.wolfram.com/PandigitalNumber.html Pandigital] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/pandigital/ Pandigital] on NUMBERSAPLENTY</ref> <ref name="xenodromic">[http://oeis.org/A010784 Xenodromes] on OEIS</ref> <ref name="smarandache">[http://mathworld.wolfram.com/SmarandacheNumber.html Smarandache number] on Wolfram Mathworld</ref> <ref name="a116700">[http://oeis.org/A116700 Early bird number] on OEIS</ref> <ref name="brilliant">[http://oeis.org/A078972 Brilliant number] on OEIS<br>•[http://www.numbersaplenty.com/set/brilliant_number/ Brilliant number] on NUMBERSAPLENTY</ref> <ref name="harshad">[http://mathworld.wolfram.com/HarshadNumber.html Harshad number] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/Harshad_number/ Harshad number] on NUMBERSAPLENTY</ref> <ref name="smith">[http://mathworld.wolfram.com/SmithNumber.html Smith number] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/Smith_number/ Smith number] on NUMBERSAPLENTY</ref> <ref name="a185186">[http://oeis.org/A185186 "Kind" number] on OEIS</ref> <ref name="a144688">[http://oeis.org/A144688 "Magic" number] on OEIS</ref> <ref name="canada">[http://www.numbersaplenty.com/set/Canada_number/ Canada number] on NUMBERSAPLENTY<!--sum of (digits^2) = sum of divisors except first and last--></ref> <ref name="repfigit">[http://mathworld.wolfram.com/KeithNumber.html Repfigit] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/repfigit_number/ Repfigit] on NUMBERSAPLENTY</ref> <ref name="rdi">[http://mathworld.wolfram.com/RecurringDigitalInvariant.html Recurring digial invariant] on Wolfram Mathworld</ref> <ref name="happy">[http://mathworld.wolfram.com/HappyNumber.html Happy number] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/happy_number/ Happy number] on NUMBERSAPLENTY</ref> <!--<ref name="unhappy">[http://mathworld.wolfram.com/UnhappyNumber.html Unhappy number] on Wolfram Mathworld</ref>--> <ref name="handsome">[http://oeis.org/A007532 Handsome number] on OEIS<br>•[http://www.numbersaplenty.com/set/d-powerful_number/ Handsome number] on NUMBERSAPLENTY</ref> <ref name="narcissistic">[http://mathworld.wolfram.com/NarcissisticNumber.html Narcissistic number] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/narcissistic_number/ Narcissistic number] on NUMBERSAPLENTY</ref> <ref name="disarium">[http://oeis.org/A032799 Disarium number] on OEIS</ref> <ref name="emirp">[http://oeis.org/a6567 emirP] on OEIS<br>•[http://www.numbersaplenty.com/set/emirp/ emirP] on NUMBERSAPLENTY</ref> <ref name="honaker">[http://www.numbersaplenty.com/set/Honaker_prime/ Honaker prime] on NUMBERSAPLENTY<!--Digit sum of n = digit sum of pi(n)--></ref> <ref name="psp">[http://mathworld.wolfram.com/FermatPseudoprime.html Fermat pseudoprime] on Wolfram Mathworld. Note: Numbers that share a prime factor with the base is usually not taken into consideration unless otherwise noted.</ref> <ref name="automorphic">[http://mathworld.wolfram.com/AutomorphicNumber.html Automorphic number] on Wolfram Mathworld<br>•[http://www.numbersaplenty.com/set/automorphic_number/ Automorphic number] on NUMBERSAPLENTY</ref> <ref name="frp"><br>[http://mathworld.wolfram.com/CyclicNumber.html Cyclic number] on Wolfram Mathworld<br>[http://mathworld.wolfram.com/FullReptendPrime.html Full Reptend Prime] on Wolfram Mathworld</ref> <ref name="homeprime">[http://mathworld.wolfram.com/HomePrime.html Home prime] on Wolfram Mathworld<!-- unfortunately missing from "digit-related" category --></ref> <ref name="ans">[http://google.com/search?q=http%3A%2F%2Fweb.archive.org%2Fweb%2F20080511154039%2Fhttp%3A%2F%2Fmy.tbaytel.net%2Fforslund%2Findex.html Bijective integer bases] from ''The Wayback Machine'' via Google</ref> <ref name="balancedternary">[http://simple.wikipedia.org/wiki/Balanced_ternary Balanced ternary] on Simple Wikipedia</ref> <ref name="friedman">[http://erich-friedman.github.io/mathmagic/0800.html Friedman numbers, Nice Friedman numbers]<br>•[http://www.numbersaplenty.com/set/Friedman_number/ Friedman numbers] on NUMBERSAPLENTY</ref> <ref name="anomalouscancellation">[http://mathworld.wolfram.com/AnomalousCancellation.html Anomalous Cancellation] on Wolfram Mathworld</ref> <ref name="almostfriedman">[http://erich-friedman.github.io/mathmagic/0713.html Fractional Friedman numbers, Redundant Friedman numbers, Almost Friedman numbers, Non-integral Friedman numbers]</ref> <ref name="friedmanpair">[http://erich-friedman.github.io/mathmagic/0619.html Anti-Friedman number, Shifted Friedman number, Friedman pair, Friedman loop]</ref> <ref name="honest">[http://erich-friedman.github.io/mathmagic/1203.html Honest mumber]</ref> <ref name="a108968">[http://oeis.org/A108968 Self-ranked number] on OEIS</ref> <!-- Non-digit related properties --> <ref name="squarefree">[http://mathworld.wolfram.com/Squarefree.html Squarefree number] on Wolfram Mathworld<sup>(1)</sup></ref> <ref name="sphenic">[http://www.numbersaplenty.com/set/sphenic_number/ Sphenic number] on NUMBERSAPLENTY<sup>(1)</sup></ref> <!-- Miscellaneous --> <ref name="technical">[http://oeis.org/wiki/Style_Sheet#Technical_definitions Divisors, aliquot parts, prime factors, prime divisors, ω, Ω, mod] on OEIS Wiki<sup>(1)</sup></ref> </references> <span style="font-size:50%"><sup>(1)</sup>Not a base-specific digit-related property</span> ==External links== * [http://www.archimedes-lab.org/numbers/Num1_69.html Numbers] on Archimedes Lab * [http://erich-friedman.github.io/numbers.html Friedman's number property list] - unfortunately, it lists only one property per number. * [http://www.numbersaplenty.com/ NUMBERSAPLENTY] (unstable)
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