A177047 Least k>1 such that n^k starts with n in base 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

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] (* Jean-François 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: A338319 A369748 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