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

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→‎9：​ Power digits
 
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__NOTOC__
__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.
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"
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<div style="border:2px solid green;">Number whose absolute value is a transcendental real 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>
<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==
==Numbers==
===0===
<div style="border:2px solid #ff00ff">
* ... is the smallest non-negative number.
* ... is the additive identity.
</div>
===1===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive number.
* ... is the multiplicative identity.
</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.
</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"/>.
</div>
===4===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive composite number.
</div>
===5===
<div style="border:2px solid blue">
* ... 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===
<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"/>.
</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 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 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 positive factors respectively.
</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 third smallest positive 1-automorphic<sub>14</sub><ref name="automorphic"/> 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 positive integer ''n'' such that 3<sup>''n''</sup> starts with three identical digits<sub>7</sub><ref name="digit"/>.
</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>.
* ... 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===
<div style="border:2px solid blue">
* ... is the smallest positive odd prime number that is not palindromic<sub>2</sub><ref name="palindromic"/>.
</div>
===12===
<div style="border:2px solid #ff00ff">
* ... is the smallest abundant number.
</div>
===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===
<div style="border:2px solid #ff00ff">
* ... is the smallest positive two-digit<sub>14</sub><ref name="digit"/> number.
</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.
</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 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 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"/>.
</div>
===21===
<div style="border:2px solid #ff00ff">
* ... 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===
<div style="border:2px solid #ff00ff">
</div>
===23===
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* ... is the smallest prime number that is not a twin prime.
</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"/>.
</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 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===
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</div>
===27===
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===28===
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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===
<div style="border:2px solid #ff00ff">
* ... 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===
<div style="border:2px solid blue">
* ... 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===
<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.
</div>
===33===
<div style="border:2px solid #ff00ff">
</div>
===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===
<div style="border:2px solid #ff00ff">
* ... 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">
</div>
===37===
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* ... is an RDI<sub>14</sub><ref name="rdi"/> of order 2.
</div>
===38===
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</div>
===39===
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</div>
===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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</div>
===42===
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===43===
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===44===
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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.
</div>
===46===
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</div>
===47===
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===48===
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===59===
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===60===
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===61===
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===62===
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===63===
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===65===
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* ..., as [http://mathworld.wolfram.com/ExpandedNotation.html 4×14+9], is a Cyclic<sub>14</sub> number<ref name="cyclic"/>.
</div>
===66===
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===80===
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==See also==
==See also==
第29行： 第1,590行：


==References==
==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>
</references>


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

2025年1月9日 (四) 17:39的最新版本

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. "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.

5

  • ... is the smallest positive odd number that is not a repunit2[4] number.
  • ... is the number of Platonic solids.

6

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

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 strobogrammaticxdi8 number.
  • ... is the number of classical elements in Shidinn culture. See Seven elements.
  • ... is the smallest known positive non-unity integer n such that there exists a three-digitn[1] number k=a×n2+b×n+c satisfying that k-1, k and k+1 have a, b and c positive factors respectively.

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 third smallest positive 1-automorphic14[5] number.

9

  • ... is the smallest positive odd composite number.
  • ... is the second smallest Smarandache7[6] number.
  • ... is the smallest positive integer n such that 3n starts with three identical digits7[1].

10

  • ... is the smallest positive even number n where n-1 is a Fermat pseudoprimen.
  • ... is the smallest positive integer that is not a Harshad7[7] number.
  • ... is a Narcissistic7[8] number.
  • ... is a strobogrammaticxdi8 number.

11

  • ... is the smallest positive odd prime number that is not palindromic2[9].

12

  • ... is the smallest abundant 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[9].

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[10] number.
  • ... is the second smallest Smarandache14[6] number.
  • ... is the smallest positive composite number whose reversal14[11] is prime.

17

  • ... is a Fermat prime.
  • ... is the smallest prime number that is the concatenation7[12] 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[11] is composite.

20

  • ... is the smallest positive integer n such that 2n is pandigital7[13].

21

  • ... is the third smallest repunit4[4] number.
  • ... is the third smallest[lɤ ɛyuə iq8 q6] positive integer whose tesseractic is a happy14[14] number.

22

23

  • ... is the smallest prime number that is not a twin prime.

24

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

25

  • ... is a narcissistic7[8] 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[11] is composite.
  • ... is the second smallest two-digit14[1] number in the Fibonacci-like sequence starting with 2 and 1.
  • ... is a repfigit14[15] number.

30

  • ... is a repdigit14[10] number.
  • ... is a strobogrammaticxdi8 number.

31

  • ... is a Mersenne prime.
  • ... is the smallest prime number that is the concatenation14[12] of two prime numbers.
  • ... is the third smallest repunit5[4] number.

32

  • ... is a repdigit7[10] number.
  • ... is a narcissistic7[8] number.

33

34

  • ... is the smallest known number in a Friedman14 loop[16]:
26=64
84=4096
6×(12×8-1)=570
2×12+10=34

35

  • ... is in a Friedman14 loop[16]:
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[16]:
122=144
4×10=40

41

42

43

44

45

  • ... is the number of letters in the Shidinn alphabet.
  • ... is a narcissistic7[8] number.
  • ... is the third smallest[lɤ ɛyuə iq8 q6] positive integer whose tesseractic is a happy7[14] number.

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

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

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

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

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


See also

Notes


References

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 Digit on Wolfram Mathworld
  2. ↑ 2.0 2.1 2.2 2.3 Recurring digial invariant on Wolfram Mathworld
  3. ↑ Full Reptend Prime on Wolfram Mathworld
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 Repunit on Wolfram Mathworld
  5. ↑ 5.0 5.1 Automorphic number on Wolfram Mathworld
  6. ↑ 6.0 6.1 Smarandache number on Wolfram Mathworld
  7. ↑ Harshad number on Wolfram Mathworld
  8. ↑ 8.0 8.1 8.2 8.3 Narcissistic number on Wolfram Mathworld
  9. ↑ 9.0 9.1 Palindromic on Wolfram Mathworld
  10. ↑ 10.0 10.1 10.2 Repdigit on Wolfram Mathworld
  11. ↑ 11.0 11.1 11.2 Reversal on Wolfram Mathworld
  12. ↑ 12.0 12.1 Concatenation on Wolfram Mathworld
  13. ↑ Pandigital on Wolfram Mathworld
  14. ↑ 14.0 14.1 Happy number on Wolfram Mathworld
  15. ↑ Repfigit on Wolfram Mathworld
  16. ↑ 16.0 16.1 16.2 Anti-Friedman number, Shifted Frieman number, Friedman pair, Friedman loop
  17. ↑ Cyclic number on Wolfram Mathworld

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

检索自“https://wiki.xdi8.top/index.php?title=User:ColorfulGalaxy/Encyclopedia_of_numbers&oldid=36804”