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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A345319 Numbers whose reciprocals have period 10.

Original entry on oeis.org

451, 1353, 2981, 4059, 8943, 9091, 26829, 27273, 81819, 100001, 122221, 300003, 366663, 372731, 900009, 1099989, 1118193, 2463661, 3354579, 4100041, 7390983, 12300123, 22172949, 27100271, 36900369, 81300813, 101010101, 243902439, 303030303, 909090909, 1111111111, 3333333333, 9999999999
Offset: 1

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Author

Tanya Khovanova, Jun 13 2021

Keywords

Comments

Equivalently, these are numbers k such that the multiplicative order of 10 modulo k is 10.
These are indices of terms at which 10 appears in A084680.
There are exactly A059892(10) = mu(10/10)*d(10^10-1) + mu(10/5)*d(10^5-1) + mu(10/2)*d(10^2-1) + mu(10/1)*d(10^1-1) = 48 - 12 - 6 + 3 = 33 terms, where d = A000005 and mu = A008683. - Jianing Song, Jun 15 2021

Examples

			1/451 = 0.00221729490022172949002217294900..., whose periodic part is 0022172949.

Crossrefs

Cf. A084680, A059892.
Subsequence of A027895.
10th row of A226477.

Programs

  • Mathematica
    Select[Range[100000000], MultiplicativeOrder[10, #] == 10 &]
  • PARI
    isok(k) = gcd(k, 10) && (znorder(Mod(10, k)) == 10); \\ Michel Marcus, Jun 14 2021
  • PARI
    my(v=divisors(10^10-1)); select(x->(znorder(Mod(10,x))==10), v) \\ Jianing Song, Jun 15 2021

Extensions

a(27)-a(28) from Jinyuan Wang, Jun 13 2021
a(29)-a(33) from Jianing Song, Jun 15 2021
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