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 A127100 #21 Jul 21 2025 16:00:49
%S A127100 1,3,9,111,333,3003003,111111111,225121209,675363627,27486820443,
%T A127100 32119664517,82460461329,24048075051027,90180273183093,
%U A127100 225346555330209,889778776887999,3336670107774441,10717272100393839,19885751580714849,27514334750263443
%N A127100 Numbers k such that k^2 divides 10^k-1.
%C A127100 Subsequence of A014950.
%C A127100 First 7 terms are palindromes. a(n) is divisible by 3 for 1<n<10. 3^2 divides a(n) for n = {3,5,6,7,9}. 37 divides a(n) for n = {4,5,7,8,9}. Prime factors of a(n) are {3,37,333667,2028119,...}. Note that a(3)/a(2) = a(5)/a(4) = a(9)/a(8) = 3 and a(7)/a(6) = 37. - _Alexander Adamchuk_, Jan 25 2007
%C A127100 Except for 3, also numbers n such that the decimal expansion of 1/n^2 has period n. - _Arkadiusz Wesolowski_, Mar 13 2012
%t A127100 Select[Range[20000], IntegerQ[(PowerMod[10, #, #^2 ]-1)/#^2 ]&]
%Y A127100 Cf. A127101, A127102, A127103, A127104, A127105, A127106, A127107, A127092, A014950.
%K A127100 nonn
%O A127100 1,2
%A A127100 _Alexander Adamchuk_, Jan 05 2007, Jan 07 2006
%E A127100 More terms from _Ryan Propper_, Jan 06 2007
%E A127100 Further terms and edited by _Max Alekseyev_, May 09 2010