

A177047


Least k>1 such that n^k starts with n in base 2.


2



2, 2, 3, 2, 8, 3, 6, 2, 7, 20, 12, 8, 4, 6, 11, 2, 13, 7, 86, 26, 19, 12, 3, 13, 15, 11, 5, 6, 8, 22, 22, 2, 24, 24, 9, 7, 25, 106, 348, 29, 15, 24, 55, 25, 60, 87, 93, 13, 84, 15, 4, 11, 12, 5, 33, 58, 324, 8, 18, 33, 44, 66, 45, 2, 46, 24, 92, 24, 38, 32, 128, 7, 59, 44, 36, 114, 16, 404
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OFFSET

1,1


COMMENTS

a(639) > 10^5.  Seiichi Manyama, Dec 22 2019


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..500


MATHEMATICA

a[n_] := For[k = 2, True, k++, If[ MatchQ[ IntegerDigits[n^k, 2], {Sequence @@ IntegerDigits[n, 2], ___}], Return[k]]]; a /@ Range[59] (* JeanFrançois Alcover, Jun 05 2013 *)


PROG

(Haskell)
toBinary 0 = []
toBinary n = toBinary (n `div` 2) ++ [odd n]
a = [2 + fromJust (findIndex (isPrefixOf (toBinary n)) [toBinary (n ^ k)  k < [2..]])  n < [1..]]
(PARI) a(n)=my(b=binary(n), k=1); while(binary(n^k++)[1..#b]!=b, ); k \\ Charles R Greathouse IV, Jun 06 2013


CROSSREFS

Cf. A051248, A177048.
Sequence in context: A345281 A338319 A280583 * A339665 A334490 A016001
Adjacent sequences: A177044 A177045 A177046 * A177048 A177049 A177050


KEYWORD

base,easy,nonn


AUTHOR

Vladimir Reshetnikov, May 01 2010


EXTENSIONS

More terms from Seiichi Manyama, Dec 22 2019


STATUS

approved



