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 A345319 Numbers whose reciprocals have period 10. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Table of n, a(n) for n=1..33. EXAMPLE 1/451 = 0.00221729490022172949002217294900..., whose periodic part is 0022172949. MATHEMATICA Select[Range[100000000], MultiplicativeOrder[10, #] == 10 &] PROG (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 CROSSREFS Cf. A084680, A059892. Subsequence of A027895. 10th row of A226477. Sequence in context: A145492 A269763 A020268 * A066322 A128922 A224560 Adjacent sequences: A345316 A345317 A345318 * A345320 A345321 A345322 KEYWORD nonn,base,easy,fini,full AUTHOR Tanya Khovanova, Jun 13 2021 EXTENSIONS a(27)-a(28) from Jinyuan Wang, Jun 13 2021 a(29)-a(33) from Jianing Song, Jun 15 2021 STATUS approved

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Last modified August 9 04:25 EDT 2024. Contains 375027 sequences. (Running on oeis4.)