Search: id:A127858
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%I A127858
%S A127858 6,66,786,9426,113106,1357266,16287186,195446226,2345354706,28144256466,
%T A127858 337731077586,4052772931026,48633275172306,583599302067666,
%U A127858 7003191624811986,84038299497743826,1008459593972925906
%N A127858 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 A127858 In base 12 the sequence is 6, 56, 556, 5556, 55556, 555556, 5555556, 
               55555556, 555555556, 5555555556. 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 since, for example, r(45^2)=r(2025)=3136=56^2=r(45)^2.
%C A127858 If a(1)=1, a(n)=12*a(n-1)-6; a(2)=12*1-6=6; a(3)=12*6-6=66 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 31 2009]
%e A127858 a(2)=66 since, in base 12, 66=56, r(56)=67 and r(56^2)=r(2630)=3741=67^2.
%Y A127858 Cf. A117755, A127856, A127857, A127859, A127860, A127861.
%Y A127858 Sequence in context: A129554 A165229 A127857 this_sequence A004355 A124862 
               A130977
%Y A127858 Adjacent sequences: A127855 A127856 A127857 this_sequence A127859 A127860 
               A127861
%K A127858 fini,nonn,base
%O A127858 1,1
%A A127858 Walter A. Kehowski (wkehowski(AT)cox.net), Feb 04 2007
%E A127858 More terms a(11)-a(19) Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Oct 31 2009

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