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%I #12 Jul 29 2023 05:01:13
%S 6,66,786,9426,113106,1357266,16287186,195446226,2345354706,
%T 28144256466,337731077586,4052772931026,48633275172306,
%U 583599302067666,7003191624811986,84038299497743826,1008459593972925906
%N Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.
%C In base 12 the sequence is 6, 56, 556, 5556, 55556, 555556, 5555556, 55555556, 555555556, 5555555556, and so on.
%C If r is the cyclic replacement map in base 10, then the only positive integers n with the property that r(n^2)=r(n)^2 appear to be 5, 45. For example, r(45^2)=r(2025)=3136=56^2=r(45)^2.
%F a(n) = 5*(12^n - 1)/11 + 1. - _Max Alekseyev_, Jul 27 2023
%e a(2)=66 since, in base 12, 66=56, r(56)=67 and r(56^2)=r(2630)=3741=67^2.
%Y Subsequence of A127857.
%Y Cf. A117755, A127856, A127859, A127860, A127861, A192544.
%K nonn,base
%O 1,1
%A _Walter Kehowski_, Feb 04 2007
%E Edited by _Max Alekseyev_, Jul 27 2023
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