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%I #32 Jun 15 2021 08:52:24
%S 451,1353,2981,4059,8943,9091,26829,27273,81819,100001,122221,300003,
%T 366663,372731,900009,1099989,1118193,2463661,3354579,4100041,7390983,
%U 12300123,22172949,27100271,36900369,81300813,101010101,243902439,303030303,909090909,1111111111,3333333333,9999999999
%N Numbers whose reciprocals have period 10.
%C Equivalently, these are numbers k such that the multiplicative order of 10 modulo k is 10.
%C These are indices of terms at which 10 appears in A084680.
%C 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
%e 1/451 = 0.00221729490022172949002217294900..., whose periodic part is 0022172949.
%t Select[Range[100000000], MultiplicativeOrder[10, #] == 10 &]
%o (PARI) isok(k) = gcd(k, 10) && (znorder(Mod(10, k)) == 10); \\ _Michel Marcus_, Jun 14 2021
%o (PARI) my(v=divisors(10^10-1)); select(x->(znorder(Mod(10,x))==10), v) \\ _Jianing Song_, Jun 15 2021
%Y Cf. A084680, A059892.
%Y Subsequence of A027895.
%Y 10th row of A226477.
%K nonn,base,easy,fini,full
%O 1,1
%A _Tanya Khovanova_, Jun 13 2021
%E a(27)-a(28) from _Jinyuan Wang_, Jun 13 2021
%E a(29)-a(33) from _Jianing Song_, Jun 15 2021
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