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A248504
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Least number k > 0 such that n^k contains 666 in its decimal representation, or 0 if no such k exists.
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1
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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
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OFFSET
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1,2
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COMMENTS
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a(n) <= a(2) = 157 for all n <= 10^5. Is there any n for which a(n) > 157? - Robert Israel, Dec 01 2014
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LINKS
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EXAMPLE
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a(2)=157 because 2^157=182687704666362864775460604089535377456991567872 contains '666' (see A007356).
a(3)=34 because 3^34=16677181699666568 contains '666' and belongs to A051003.
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MAPLE
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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;
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MATHEMATICA
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A248504[n_] := If[IntegerQ[Log10[n]], 0, Block[{k = 0}, While[StringFreeQ[IntegerString[n^++k], "666"]]; k]];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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