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 A334603 #31 Nov 19 2023 21:17:31
%S A334603 2,22,242,2662,29282,322102,3543122,38974342,428717762,4715895382,
%T A334603 51874849202,570623341222,6276856753442,69045424287862,
%U A334603 759499667166482,8354496338831302,91899459727144322,1010894056998587542,11119834626984462962,122318180896829092582
%N A334603 Period of the fraction 1/11^n for n >= 1.
%C A334603 Conjecture proposed by the authors in References page 205: if p is a prime with gcd(p,30) = 1 and if the period of 1/p is m then the period of 1/p^n is m*p^(n-1).
%D A334603 J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 346 pp. 50, 204-205, Ellipses, Paris 2004.
%F A334603 a(n) = 2 * 11^(n-1) [conjectured, see comments].
%F A334603 a(n) = A051626(A001020(n)).
%e A334603 1/121 = 0. 0082644628099173553719 0082644628099173553719 ... with periodic part {0082644628099173553719}, whose length is 22 digits, so a(2) = 22.
%t A334603 MultiplicativeOrder[10, 11^#] & /@ Range[20] (* _Giovanni Resta_, May 07 2020 *)
%o A334603 (PARI) a(n) = znorder(Mod(10, 11^n)); \\ _Michel Marcus_, May 09 2020
%Y A334603 Cf. period of fractions: A051626 (1/n), A133494 (1/3^n), A055272 (1/7^n).
%Y A334603 Cf. A001020 (11^n).
%K A334603 nonn,base
%O A334603 1,1
%A A334603 _Bernard Schott_, May 07 2020
%E A334603 More terms from _Giovanni Resta_, May 07 2020