查看“User:ColorfulGalaxy/Encyclopedia of numbers”的源代码

__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 are also welcome.

{| border="0" class="toccolours wikitable"
|-
! colspan="9" | {{MediaWiki:Toc}}
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| align="center" | [[#0|0]] || [[#1|1]] || [[#2|2]] || [[#7|7]] || [[#14|14]] || [[#49|49]] || [[#196|196]] || [[#343|343]] || [[#2744|2744]] __NOTOC__
|-
| align="center" colspan="9" | [[#top|Top of page]] &mdash; [[#Legend|Legend]] &mdash; [[#See also|See also]] &mdash; [[#External links|External links]]
|}

==Legend==

<div style="border:2px solid blue;">Positive prime numbers </div>
<div style="border:2px solid #ff00ff;">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 #00ffff;">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. "Digit<sub>14</sub>"<ref name="digit"/> is read as "tetradecimal digit".

==Numbers==

===0===
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* ... is the smallest non-negative number.
* ... is the additive identity.
</div>

===1===
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* ... is the smallest positive number.
* ... is the multiplicative identity.
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===2===
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* ... 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.
</div>

===3===
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* ... is the smallest odd positive prime number.
* ... is the smallest Full Reptend Prime<sub>14</sub><ref name="frp"/>.
</div>

===4===
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* ... is the smallest positive composite number.
</div>

===5===
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* ... is the smallest positive odd number that is not a repunit<sup>2</sup><ref name="repunit"/> number.
* ... is the number of Platonic solids.
</div>

===6===
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* ... is the smallest positive composite number that is not a perfect power.
* ... is the largest digit<sub>7</sub><ref name="digit"/>.
</div>

===7===
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* ... 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 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]].
</div>

===8===
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* ... 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 third smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> number.
</div>

===9===
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* ... is the smallest positive odd composite number.
* ... is the second smallest Smarandache<sub>7</sub><ref name="smarandache"/> number.
</div>

===10===
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* ... is the smallest positive even number ''n'' where ''n''-1 is a Fermat pseudoprime<sub>''n''</sub>.
* ... is the smallest positive integer that is not a Harshad<sub>7</sub><ref name="harshad"/> number.
* ... is a Narcissistic<sub>7</sub><ref name="narcissistic"/> number.
* ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
</div>

===11===
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* ... is the smallest positive odd prime number that is not palindromic<sub>2</sub><ref name="palindromic"/>.
</div>

===12===
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* ... is the smallest abundant number.
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===13===
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* ... 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"/>.
</div>

===14===
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* ... is the smallest positive two-digit<sub>14</sub><ref name="digit"/> number.
</div>

===15===
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* ... 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.
</div>

===16===
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* ... 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 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===
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* ... 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===
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* ... is the smallest two-digit<sub>14</sub><ref name="digit"/> number in the Fibonacci-like sequence starting with 2 and 1.
</div>

===19===
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* ... is the smallest positive odd prime number whose reversal<sub>2</sub><ref name="reversal"/> is composite.
</div>

===20===
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* ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> is pandigital<sub>7</sub><ref name="pandigital"/>.
</div>

===21===
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* ... is the third smallest repunit<sub>4</sub><ref name="repunit"/> number.
* ... is the third smallest<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup> positive integer whose tesseractic is a happy<sub>14</sub><ref name="happy"/> number.
</div>

===22===
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===23===
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* ... is the smallest prime number that is not a twin prime.
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===24===
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* ... is the smallest positive integer ''n'' such that 2<sup>''n''</sup> ends in three identical digits<sub>7</sub><ref name="digit"/>.
</div>

===25===
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* ... 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 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>.
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===29===
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* ... is the smallest positive odd prime number whose reversal<sub>14</sub><ref name="reversal"/> is composite.
* ... 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===
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* ... is a repdigit<sub>14</sub><ref name="repdigit"/> number.
* ... is a strobogrammatic<sub>[[希顶字母数字|xdi8]]</sub> number.
</div>

===31===
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* ... is a Mersenne prime.
* ... is the smallest prime number that is the concatenation<sub>14</sub><ref name="concatenation"/> of two prime numbers.
* ... is the third smallest repunit<sub>5</sub><ref name="repunit"/> number.
</div>

===32===
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* ... is a repdigit<sub>7</sub><ref name="repdigit"/> number.
* ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number.
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===33===
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===34===
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* ... 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===
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* ... 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===
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===37===
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* ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2.
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===38===
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===40===
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* ... is in a Friedman<sub>14</sub> pair<ref name="friedmanpair"/>:
:: 12<sup>2</sup>=144
:: 4&times;10=40
</div>

===41===
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===45===
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* ... is the number of letters in the [[Shidinn alphabet]].
* ... is a narcissistic<sub>7</sub><ref name="narcissistic"/> number.
* ... is the third smallest<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup> positive integer whose tesseractic is a happy<sub>7</sub><ref name="happy"/> number.
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* ..., as [http://mathworld.wolfram.com/ExpandedNotation.html 4×14+9], is a Cyclic<sub>14</sub> number<ref name="cyclic"/>. 
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==See also==

==Notes==
<references group="note">
</references>

==References==
<references><ref name="digit">[http://mathworld.wolfram.com/Digit.html Digit] 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="palindromic">[http://mathworld.wolfram.com/PalindromicNumber.html Palindromic] on Wolfram Mathworld</ref>
<ref name="repdigit">[http://mathworld.wolfram.com/Repdigit.html Repdigit] on Wolfram Mathworld</ref>
<ref name="repunit">[http://mathworld.wolfram.com/Repunit.html Repunit] on Wolfram Mathworld</ref>
<ref name="pandigital">[http://mathworld.wolfram.com/PandigitalNumber.html Pandigital] on Wolfram Mathworld</ref>
<ref name="smarandache">[http://mathworld.wolfram.com/SmarandacheNumber.html Smarandache number] on Wolfram Mathworld</ref>
<ref name="harshad">[http://mathworld.wolfram.com/HarshadNumber.html Harshad number] on Wolfram Mathworld</ref>
<ref name="repfigit">[http://mathworld.wolfram.com/KeithNumber.html Repfigit] on Wolfram Mathworld</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</ref>
<ref name="unhappy">[http://mathworld.wolfram.com/UnhappyNumber.html Unhappy number] on Wolfram Mathworld</ref>
<ref name="narcissistic">[http://mathworld.wolfram.com/NarcissisticNumber.html Narcissistic number] on Wolfram Mathworld</ref>
<ref name="automorphic">[http://mathworld.wolfram.com/AutomorphicNumber.html Automorphic number] on Wolfram Mathworld</ref>
<ref name="cyclic">[http://mathworld.wolfram.com/CyclicNumber.html Cyclic number] on Wolfram Mathworld</ref>
<ref name="frp">[http://mathworld.wolfram.com/FullReptendPrime.html Full Reptend Prime] on Wolfram Mathworld</ref>
<ref name="friedman">[http://erich-friedman.github.io/mathmagic/0800.html Friedman numbers, Nice Friedman numbers]</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 Frieman number, Friedman pair, Friedman loop]</ref>
</references>

==External links==
* [http://www.archimedes-lab.org/numbers/Num1_69.html Numbers] on Archimedes Lab