login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A248504
Least number k > 0 such that n^k contains 666 in its decimal representation, or 0 if no such k exists.
1
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
1,2
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
LINKS
EXAMPLE
a(2)=157 because 2^157=182687704666362864775460604089535377456991567872 contains '666' (see A007356).
a(3)=34 because 3^34=16677181699666568 contains '666' and belongs to A051003.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A216788 A239338 A028675 * A090851 A045230 A180551
KEYWORD
nonn,base,less
AUTHOR
Talha Ali, Dec 01 2014
EXTENSIONS
More terms from Alois P. Heinz, Dec 01 2014
STATUS
approved