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

0, 157, 34, 96, 102, 18, 70, 64, 17, 0, 42, 41, 25, 44, 30, 48, 16, 97, 30, 157, 50, 33, 15, 35, 51, 12, 35, 10, 34, 34, 34, 44, 44, 30, 47, 9, 20, 46, 23, 96, 33, 13, 42, 32, 39, 17, 8, 27, 35, 102, 22, 42, 80, 55, 28, 55, 38, 19, 48, 18, 74, 15, 31, 32, 37

Offset: 1

Author

Talha Ali, Dec 01 2014

Keywords

• nonn
• base
• less

Comments

a(n) <= a(2) = 157 for all n <= 10^5. Is there any n for which a(n) > 157? - Robert Israel, Dec 01 2014

Examples

			a(2)=157 because 2^157=182687704666362864775460604089535377456991567872 contains '666' (see A007356).
a(3)=34 because 3^34=16677181699666568 contains '666' and belongs to A051003.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007356, A051003.

Programs

Maple

f:= proc(n)
local k;
if n = 10^ilog10(n) then return 0 fi;
for k from 1 do
  if StringTools[Search]("666",sprintf("%d",n^k)) <> 0 then return k fi
od
end proc;
seq(f(n), n=1..1000); # Robert Israel, Dec 01 2014

Mathematica

A248504[n_] := If[IntegerQ[Log10[n]], 0, Block[{k = 0}, While[StringFreeQ[IntegerString[n^++k], "666"]]; k]];
Array[A248504, 100] (* Paolo Xausa, Apr 08 2024 *)

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);}
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

Extensions

More terms from Alois P. Heinz, Dec 01 2014