User:ColorfulGalaxy/Encyclopedia of numbers：修订间差异

2025年1月18日 (六) 16:20的版本

This article is inspired by 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-related entries are also welcome.

目录
0	1	2	7	14	49	196	343	2744
Top of page — Legend — See also — External links

Legend

Positive prime numbers

Number (excluding positive prime numbers) whose absolute value is an integer

Number whose absolute value is a rational number that is not integer

Number whose absolute value is an algebraic irrational number

Number whose absolute value is a transcendental real number

Unknown/approximation

Some terms can have subscripts. For example, "digit₁₄"^[1] is read as "tetradecimal digit".

Numbers

0

... is the smallest non-negative number.
... is the additive identity.

1

... is the smallest positive number.
... is the multiplicative identity.

2

... is the smallest positive prime number.
... is the only even positive prime number.
... is an RDI₇^[2] of order 2.

3

... is the smallest odd positive prime number.
... is the smallest Full Reptend Prime₁₄^[3].

4

... is the smallest positive composite number.
... is the 2nd square number.

5

... is the smallest positive odd number that is not a repunit₂^[4] number.
... is the number of Platonic solids.
... was the number of members in the Shidinn community administration committee when it started.

6

... is the smallest positive composite number that is not a perfect power.
... is the largest digit₇^[1].
... is the smallest perfect number.

7

... is the third smallest repunit₂^[4] number.
... is the smallest positive two-digit₇^[1] number.
... is the second smallest positive 1-automorphic₁₄^[5] number.
... is the smallest positive strobogrammatic_xdi8 number.
... is the number of classical elements in Shidinn culture. See Seven elements.
... is the smallest positive non-unity integer n such that there exists a four-digit_n^[1] repdigit_n^[6] square number.
... is the smallest known positive non-unity integer n such that there exists a three-digit_n^[1] number k=a×n²+b×n+c satisfying that k-1, k and k+1 have a, b and c (i. e. its digits) positive factors respectively.
... is the number of God in western culture.

8

... 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 repunit₇^[4] number.
... is the smallest known repfigit₇^[7] number.
... is the third smallest positive 1-automorphic₁₄^[5] number.
... is the second cubic number.

9

... is the smallest positive odd composite number.
... is the second smallest Smarandache₇^[8] number.
... is the smallest positive integer n such that 3ⁿ starts with three identical digits₇^[1].
... is the smallest positive integer n such that nⁿ is pandigital₇^[9].
... is the largest digit in base-10.

10

... is the smallest positive even number n where n-1 is a Fermat pseudoprime_n.
... is the smallest positive integer that is not a Harshad₇^[10] number.
... is a Narcissistic₇^[11] number.
... is a disarium₇^[12] number.
... is a strobogrammatic_xdi8 number.
... is the number of current members in the Shidinn community administration committee.

11

... is the smallest positive odd prime number that is not palindromic₂^[13].

12

... is the smallest abundant number.
... is the smallest known positive non-unity integer n such that there exists a five-digit_n^[1] number k=a×n⁴+b×n³+c×n²+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 repdigit₁₂^[6] number.
... is the smallest true composite number.

13

... is the number of Archimedean solids.
... is the largest digit₁₄^[1].
... is the third smallest repunit₃^[4] number.
... is an RDI₇^[2] of order 2.
... is the smallest positive odd Fibonacci number that is not palindromic₂^[13].
... is the number of Devil in western culture.

14

... is the smallest positive two-digit₁₄^[1] number.

15

... is the smallest positive odd composite number that is not a perfect power.
... is the second smallest repunit₁₄^[4] number.

16

... is the second smallest positive tesseractic number.
... is the smallest positive integer with five positive factors.
... is a repdigit₇^[6] number.
... is the second smallest Smarandache₁₄^[8] number.
... is the smallest positive composite number whose reversal₁₄^[14] is prime.

17

... is a Fermat prime.
... is the smallest prime number that is the concatenation₇^[15] of two prime numbers.

18

... is the smallest two-digit₁₄^[1] number in the Fibonacci-like sequence starting with 2 and 1.

19

... is the smallest positive odd prime number whose reversal₂^[14] is composite.

20

... is the smallest positive integer n such that 2ⁿ is pandigital₇^[9].
... is the smallest positive non-repdigit₇ integer whose square is repdigit₇^[6].

21

... is the third smallest repunit₄^[4] number.
... is the third smallest^{[lɤ ɛyuə iq8 q6]} positive integer whose tesseractic is a happy₁₄^[16] number.

22

23

... is the smallest prime number that is not a twin prime.
... is the smaller prime factor of 2047, the smallest Mersenne composite number.

24

... is the smallest positive integer n such that 2ⁿ ends in three identical digits₇^[1].

25

... is a narcissistic₇^[11] number.
... is an RDI₁₄^[2] of order 2.
... is the smallest positive integer n such that 2ⁿ starts in three identical digits₇^[1] and ends in three identical digits₇.

26

27

28

29

... is the smallest positive odd prime number whose reversal₁₄^[14] is composite.
... is the second smallest two-digit₁₄^[1] number in the Fibonacci-like sequence starting with 2 and 1.
... is a repfigit₁₄^[7] number.

30

... is a repdigit₁₄^[6] number.
... is a strobogrammatic_xdi8 number.

31

... is a Mersenne prime.
... is the smallest prime number that is the concatenation₁₄^[15] of two prime numbers.
... is the third smallest repunit₅^[4] number.

32

... is a repdigit₇^[6] number.
... is a narcissistic₇^[11] number.

33

34

... is the smallest known number in a Friedman₁₄ loop^[17]:

2⁶=64

8⁴=4096

6×(12×8-1)=570

2×12+10=34

35

... is in a Friedman₁₄ loop^[17]:

7³=343

(1+10)×7=77

5×7=35

7²=49

36

37

... is an RDI₁₄^[2] of order 2.

38

39

40

... is in a Friedman₁₄ pair^[17]:

12²=144

4×10=40

41

42

43

44

45

... is the number of letters in the Shidinn alphabet.
... is a narcissistic₇^[11] number.
... is the third smallest^{[lɤ ɛyuə iq8 q6]} positive integer whose tesseractic is a happy₇^[16] number.

46

47

... is the largest two-digit₇^[1] prime number.
... is the representative prime number of User:Rachel1211.

48

... is the largest two-digit₇^[1] number.

49

... is the smallest three-digit₇^[1] number.

50

... is the smallest positive palindromic₇^[13] number that is not repdigit₇^[6].

51

52

53

... is the smallest three-digit₇^[1] prime number.

54

55

56

57

... is the third smallest repunit₇^[4] number.

58

59

60

61

62

63

64

65

..., as 4×14+9, is a Cyclic₁₄ number^[18].

66

... is the third smallest Smarandache₇^[8] number.

67

68

69

70

71

... is the smallest positive palindromic₇^[13] prime number that is not repdigit₇^[6].

72

73

... is the third smallest repunit₈^[4] number.
... is the third smallest positive integer that is both palindromic₂^[13] and palindromic_b3^[19].
... 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 a number worshipped in Shidinn culture.
... is featured on this website. You can submit entries there.

74

75

76

77

78

79

80

81

... is the third smallest positive tesseractic number.
... is in the username of User:DGCK81LNN.

82

... is a strobogrammatic_xdi8 number.

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

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131

132

133

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135

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144

145

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148

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151

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155

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157

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163

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300

Notes

References

↑ ^{跳转到： 1.00} ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 ^1.10 ^1.11 ^1.12 ^1.13 ^1.14 ^1.15 ^1.16 Digit on Wolfram Mathworld
↑ ^{跳转到： 2.0} ^2.1 ^2.2 ^2.3 Recurring digial invariant on Wolfram Mathworld
↑ Full Reptend Prime on Wolfram Mathworld
↑ ^{跳转到： 4.0} ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 ^4.6 ^4.7 ^4.8 Repunit on Wolfram Mathworld
↑ ^{跳转到： 5.0} ^5.1 Automorphic number on Wolfram Mathworld
↑ ^{跳转到： 6.0} ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 ^6.6 ^6.7 Repdigit on Wolfram Mathworld
↑ ^{跳转到： 7.0} ^7.1 Repfigit on Wolfram Mathworld
↑ ^{跳转到： 8.0} ^8.1 ^8.2 Smarandache number on Wolfram Mathworld
↑ ^{跳转到： 9.0} ^9.1 Pandigital on Wolfram Mathworld
↑ Harshad number on Wolfram Mathworld
↑ ^{跳转到： 11.0} ^11.1 ^11.2 ^11.3 Narcissistic number on Wolfram Mathworld
↑ Disarium number on OEIS
↑ ^{跳转到： 13.0} ^13.1 ^13.2 ^13.3 ^13.4 Palindromic on Wolfram Mathworld
↑ ^{跳转到： 14.0} ^14.1 ^14.2 Reversal on Wolfram Mathworld
↑ ^{跳转到： 15.0} ^15.1 Concatenation on Wolfram Mathworld
↑ ^{跳转到： 16.0} ^16.1 Happy number on Wolfram Mathworld
↑ ^{跳转到： 17.0} ^17.1 ^17.2 Anti-Friedman number, Shifted Frieman number, Friedman pair, Friedman loop
↑ Cyclic number on Wolfram Mathworld
↑ Balanced ternary on Simple Wikipedia

引用错误：<references>内定义的name（名称）为“unhappy”的<ref>标签未在前文内使用。
引用错误：<references>内定义的name（名称）为“friedman”的<ref>标签未在前文内使用。
引用错误：<references>内定义的name（名称）为“almostfriedman”的<ref>标签未在前文内使用。

External links

Numbers on Archimedes Lab

[digit-1] {跳转到： 1.00} ^1.01 ^1.02 ^1.03 ^1.04 ^1.05 ^1.06 ^1.07 ^1.08 ^1.09 ^1.10 ^1.11 ^1.12 ^1.13 ^1.14 ^1.15 ^1.16 Digit on Wolfram Mathworld

[rdi-2] {跳转到： 2.0} ^2.1 ^2.2 ^2.3 Recurring digial invariant on Wolfram Mathworld

[frp-3] Full Reptend Prime on Wolfram Mathworld

[repunit-4] {跳转到： 4.0} ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 ^4.6 ^4.7 ^4.8 Repunit on Wolfram Mathworld

[automorphic-5] {跳转到： 5.0} ^5.1 Automorphic number on Wolfram Mathworld

[repdigit-6] {跳转到： 6.0} ^6.1 ^6.2 ^6.3 ^6.4 ^6.5 ^6.6 ^6.7 Repdigit on Wolfram Mathworld

[repfigit-7] {跳转到： 7.0} ^7.1 Repfigit on Wolfram Mathworld

[smarandache-8] {跳转到： 8.0} ^8.1 ^8.2 Smarandache number on Wolfram Mathworld

[pandigital-9] {跳转到： 9.0} ^9.1 Pandigital on Wolfram Mathworld

[harshad-10] Harshad number on Wolfram Mathworld

[narcissistic-11] {跳转到： 11.0} ^11.1 ^11.2 ^11.3 Narcissistic number on Wolfram Mathworld

[disarium-12] Disarium number on OEIS

[palindromic-13] {跳转到： 13.0} ^13.1 ^13.2 ^13.3 ^13.4 Palindromic on Wolfram Mathworld

[reversal-14] {跳转到： 14.0} ^14.1 ^14.2 Reversal on Wolfram Mathworld

[concatenation-15] {跳转到： 15.0} ^15.1 Concatenation on Wolfram Mathworld

[happy-16] {跳转到： 16.0} ^16.1 Happy number on Wolfram Mathworld

[friedmanpair-17] {跳转到： 17.0} ^17.1 ^17.2 Anti-Friedman number, Shifted Frieman number, Friedman pair, Friedman loop

[cyclic-18] Cyclic number on Wolfram Mathworld

[balancedternary-19] Balanced ternary on Simple Wikipedia

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

@@ 第52行： / 第52行： @@
 <div style="border:2px solid #ff00ff">
 * ... is the smallest positive composite number.
+* ... is the 2nd square number.
 </div>
@@ 第65行： / 第66行： @@
 * ... 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.
 </div>
@@ 第76行： / 第78行： @@
 * ... 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.
+* ... is the number of God in western culture.
 </div>
@@ 第86行： / 第89行： @@
 * ... 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 second cubic number.
 </div>
@@ 第94行： / 第98行： @@
 * ... 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 the largest digit in base-10.
 </div>
@@ 第115行： / 第120行： @@
 * ... is the smallest abundant number.
 * ... 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>
@@ 第124行： / 第130行： @@
 * ... 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 the number of Devil in western culture.
 </div>