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.
%I A345319 #32 Jun 15 2021 08:52:24 %S A345319 451,1353,2981,4059,8943,9091,26829,27273,81819,100001,122221,300003, %T A345319 366663,372731,900009,1099989,1118193,2463661,3354579,4100041,7390983, %U A345319 12300123,22172949,27100271,36900369,81300813,101010101,243902439,303030303,909090909,1111111111,3333333333,9999999999 %N A345319 Numbers whose reciprocals have period 10. %C A345319 Equivalently, these are numbers k such that the multiplicative order of 10 modulo k is 10. %C A345319 These are indices of terms at which 10 appears in A084680. %C A345319 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 A345319 1/451 = 0.00221729490022172949002217294900..., whose periodic part is 0022172949. %t A345319 Select[Range[100000000], MultiplicativeOrder[10, #] == 10 &] %o A345319 (PARI) isok(k) = gcd(k, 10) && (znorder(Mod(10, k)) == 10); \\ _Michel Marcus_, Jun 14 2021 %o A345319 (PARI) my(v=divisors(10^10-1)); select(x->(znorder(Mod(10,x))==10), v) \\ _Jianing Song_, Jun 15 2021 %Y A345319 Cf. A084680, A059892. %Y A345319 Subsequence of A027895. %Y A345319 10th row of A226477. %K A345319 nonn,base,easy,fini,full %O A345319 1,1 %A A345319 _Tanya Khovanova_, Jun 13 2021 %E A345319 a(27)-a(28) from _Jinyuan Wang_, Jun 13 2021 %E A345319 a(29)-a(33) from _Jianing Song_, Jun 15 2021