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A248504 Least number k > 0 such that n^k contains 666 in its decimal representation, or 0 if no such k exists.

%I A248504 #31 Apr 08 2024 17:47:55
%S A248504 0,157,34,96,102,18,70,64,17,0,42,41,25,44,30,48,16,97,30,157,50,33,
%T A248504 15,35,51,12,35,10,34,34,34,44,44,30,47,9,20,46,23,96,33,13,42,32,39,
%U A248504 17,8,27,35,102,22,42,80,55,28,55,38,19,48,18,74,15,31,32,37
%N A248504 Least number k > 0 such that n^k contains 666 in its decimal representation, or 0 if no such k exists.
%C A248504 a(n) <= a(2) = 157 for all n <= 10^5.  Is there any n for which a(n) > 157? - _Robert Israel_, Dec 01 2014
%H A248504 Alois P. Heinz, <a href="/A248504/b248504.txt">Table of n, a(n) for n = 1..10000</a>
%e A248504 a(2)=157 because 2^157=182687704666362864775460604089535377456991567872 contains '666' (see A007356).
%e A248504 a(3)=34 because 3^34=16677181699666568 contains '666' and belongs to A051003.
%p A248504 f:= proc(n)
%p A248504 local k;
%p A248504 if n = 10^ilog10(n) then return 0 fi;
%p A248504 for k from 1 do
%p A248504   if StringTools[Search]("666",sprintf("%d",n^k)) <> 0 then return k fi
%p A248504 od
%p A248504 end proc;
%p A248504 seq(f(n), n=1..1000); # _Robert Israel_, Dec 01 2014
%t A248504 A248504[n_] := If[IntegerQ[Log10[n]], 0, Block[{k = 0}, While[StringFreeQ[IntegerString[n^++k], "666"]]; k]];
%t A248504 Array[A248504, 100] (* _Paolo Xausa_, Apr 08 2024 *)
%o A248504 (PARI) isok(n) = {d = digits(n); for (i=1, #d-3, if ((d[i] == 6) && (d[i+1]==6) && (d[i+2]==6), return(1));); return (0);}
%o A248504 a(n) = {if ((n==1) || (n==10) || (ispower(n,,&p) && (p==10)), return(0)); k = 1; while (! isok(n^k), k++); k;} \\ _Michel Marcus_, Dec 01 2014
%Y A248504 Cf. A007356, A051003.
%K A248504 nonn,base,less
%O A248504 1,2
%A A248504 _Talha Ali_, Dec 01 2014
%E A248504 More terms from _Alois P. Heinz_, Dec 01 2014