A248504 - OEIS

%I #31 Apr 08 2024 17:47:55

%S 0,157,34,96,102,18,70,64,17,0,42,41,25,44,30,48,16,97,30,157,50,33,

%T 15,35,51,12,35,10,34,34,34,44,44,30,47,9,20,46,23,96,33,13,42,32,39,

%U 17,8,27,35,102,22,42,80,55,28,55,38,19,48,18,74,15,31,32,37

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

%C 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 Alois P. Heinz, <a href="/A248504/b248504.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2)=157 because 2^157=182687704666362864775460604089535377456991567872 contains '666' (see A007356).

%e a(3)=34 because 3^34=16677181699666568 contains '666' and belongs to A051003.

%p f:= proc(n)

%p local k;

%p if n = 10^ilog10(n) then return 0 fi;

%p for k from 1 do

%p   if StringTools[Search]("666",sprintf("%d",n^k)) <> 0 then return k fi

%p od

%p end proc;

%p seq(f(n), n=1..1000); # _Robert Israel_, Dec 01 2014

%t A248504[n_] := If[IntegerQ[Log10[n]], 0, Block[{k = 0}, While[StringFreeQ[IntegerString[n^++k], "666"]]; k]];

%t Array[A248504, 100] (* _Paolo Xausa_, Apr 08 2024 *)

%o (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 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 Cf. A007356, A051003.

%K nonn,base,less

%O 1,2

%A _Talha Ali_, Dec 01 2014

%E More terms from _Alois P. Heinz_, Dec 01 2014