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

2025年2月16日 (日) 21:56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.
... 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.

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 that represents 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 that represents Devil in western culture.

14

... is the smallest positive two-digit₁₄^[1] number.
... is the index of the nasal sibilant in the Shidinn alphabet.

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 sum of all the one-digit₇^[1] numbers. It is also the numbers of dots on a dice.
... 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

... is the sum of all the one-digit₁₄^[1] prime numbers.

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.
... is the sum of all the one-digit₁₄^[1] composite numbers.

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

... 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.

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

... is the sum of the first three Smarandache₇^[8] numbers.

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

... is the total number of letters in the Shidinn alphabet and the Extended Shidinn alphabet, including the "number zero" letter.

90

91

... is the sum of all the one-digit₁₄^[1] numbers.
... is the third smallest repunit₉^[4] number.

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

... is a number worshipped in Shidinn culture.^{[lɤ ɛyuə iq8 q6]}

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

... is the largest two-digit₁₄^[1] prime number.

194

195

... is the largest two-digit₁₄^[1] number.

196

... is the smallest three-digit₁₄^[1] number.

197

... is the smallest three-digit₁₄^[1] prime number.
... is the smallest positive palindromic₁₄^[13] number that is not repdigit₁₄^[6].
... is the smallest positive palindromic₁₄^[13] prime number that is not repdigit₁₄^[6].

198

199

200

201

... is the smallest three-digit₁₄^[1] squarefree composite number.

202

203

204

205

206

207

208

209

210

211

... is the third smallest repunit₁₄^[4] number.
... is the smallest repunit₁₄^[4] prime number.

212

213

214

215

216

217

218

219

220

221

222

223

224

225

... is the second smallest three-digit₁₄^[1] square number.

226

227

... is the third smallest Smarandache₁₄^[8] number, as well as the smallest Smarandache₁₄ 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.

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

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 ^1.17 ^1.18 ^1.19 ^1.20 ^1.21 ^1.22 ^1.23 ^1.24 ^1.25 ^1.26 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： 4.00} ^4.01 ^4.02 ^4.03 ^4.04 ^4.05 ^4.06 ^4.07 ^4.08 ^4.09 ^4.10 ^4.11 Repunit on Wolfram Mathworld
↑ ^{跳转到： 5.0} ^5.1 Automorphic number on Wolfram Mathworld
↑ ^{跳转到： 6.00} ^6.01 ^6.02 ^6.03 ^6.04 ^6.05 ^6.06 ^6.07 ^6.08 ^6.09 Repdigit on Wolfram Mathworld
↑ ^{跳转到： 7.0} ^7.1 Repfigit on Wolfram Mathworld
↑ ^{跳转到： 8.0} ^8.1 ^8.2 ^8.3 ^8.4 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 ^13.5 ^13.6 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 Friedman number, Friedman pair, Friedman loop
↑ Cyclic number on Wolfram Mathworld
↑ Balanced ternary on Simple Wikipedia

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 ^1.17 ^1.18 ^1.19 ^1.20 ^1.21 ^1.22 ^1.23 ^1.24 ^1.25 ^1.26 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： 4.00} ^4.01 ^4.02 ^4.03 ^4.04 ^4.05 ^4.06 ^4.07 ^4.08 ^4.09 ^4.10 ^4.11 Repunit on Wolfram Mathworld

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

[repdigit-6] {跳转到： 6.00} ^6.01 ^6.02 ^6.03 ^6.04 ^6.05 ^6.06 ^6.07 ^6.08 ^6.09 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 ^8.3 ^8.4 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 ^13.5 ^13.6 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 Friedman 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79行： / 第79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.
+* ... is the number that represents God in western culture.
 </div>
@@ 第131行： / 第131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.
+* ... is the number that represents Devil in western culture.
 </div>
@@ 第137行： / 第137行： @@
 <div style="border:2px solid #ff00ff">
 * ... is the smallest positive two-digit<sub>14</sub><ref name="digit"/> number.
+* ... is the index of the nasal sibilant in the [[Shidinn alphabet]].
 </div>
@@ 第178行： / 第179行： @@
 ===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 a dice.
 * ... 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.
@@ 第298行： / 第300行： @@
 ===41===
 <div style="border:2px solid blue">
+* ... is the sum of all the one-digit<sub>14</sub><ref name="digit"/> prime numbers.
 </div>
@@ 第342行： / 第344行： @@
 <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.
 </div>
@@ 第391行： / 第394行： @@
 ===59===
 <div style="border:2px solid blue">
+* ... 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>
@@ 第480行： / 第483行： @@
 ===76===
 <div style="border:2px solid #ff00ff">
+* ... is the sum of the first three Smarandache<sub>7</sub><ref name="smarandache"/> numbers.
 </div>
@@ 第546行： / 第549行： @@
 ===89===
 <div style="border:2px solid blue">
+* ... is the total number of letters in the [[Shidinn alphabet]] and the Extended Shidinn alphabet, including the "number zero" letter.
 </div>
@@ 第556行： / 第559行： @@
 ===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.
 </div>
@@ 第736行： / 第740行： @@
 ===127===
 <div style="border:2px solid blue">
+* ... is a number worshipped in Shidinn culture.<sup>&#91;lɤ ɛyuə iq<small><small>8</small></small> q<small><small>6</small></small>&#93;</sup>
 </div>
@@ 第1,066行： / 第1,070行： @@
 ===193===
 <div style="border:2px solid blue">
+* ... is the largest two-digit<sub>14</sub><ref name="digit"/> prime number.
 </div>
@@ 第1,076行： / 第1,080行： @@
 ===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"/>.
 </div>
@@ 第1,106行： / 第1,112行： @@
 ===201===
 <div style="border:2px solid #ff00ff">
+* ... is the smallest three-digit<sub>14</sub><ref name="digit"/> squarefree composite number.
 </div>
@@ 第1,156行： / 第1,162行： @@
 ===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>
@@ 第1,226行： / 第1,233行： @@
 ===225===
 <div style="border:2px solid #ff00ff">
+* ... is the second smallest three-digit<sub>14</sub><ref name="digit"/> square number.
 </div>
@@ 第1,236行： / 第1,243行： @@
 ===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>
@@ 第1,634行： / 第1,642行： @@
 <!--<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>
+<ref name="friedmanpair">[http://erich-friedman.github.io/mathmagic/0619.html Anti-Friedman number, Shifted Friedman number, Friedman pair, Friedman loop]</ref>
 </references>
 ==External links==
 * [http://www.archimedes-lab.org/numbers/Num1_69.html Numbers] on Archimedes Lab