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
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..500
Programs
-
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..]]
-
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 *) -
PARI
a(n)=my(b=binary(n),k=1);while(binary(n^k++)[1..#b]!=b,);k \\ Charles R Greathouse IV, Jun 06 2013
Extensions
More terms from Seiichi Manyama, Dec 22 2019
Comments