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%I #19 Dec 22 2019 19:11:26
%S 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,
%T 22,22,2,24,24,9,7,25,106,348,29,15,24,55,25,60,87,93,13,84,15,4,11,
%U 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
%N Least k>1 such that n^k starts with n in base 2.
%C a(639) > 10^5. - _Seiichi Manyama_, Dec 22 2019
%H Seiichi Manyama, <a href="/A177047/b177047.txt">Table of n, a(n) for n = 1..500</a>
%t 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 *)
%o (Haskell)
%o toBinary 0 = []
%o toBinary n = toBinary (n `div` 2) ++ [odd n]
%o a = [2 + fromJust (findIndex (isPrefixOf (toBinary n)) [toBinary (n ^ k) | k <- [2..]]) | n <- [1..]]
%o (PARI) a(n)=my(b=binary(n),k=1);while(binary(n^k++)[1..#b]!=b,);k \\ _Charles R Greathouse IV_, Jun 06 2013
%Y Cf. A051248, A177048.
%K base,easy,nonn
%O 1,1
%A _Vladimir Reshetnikov_, May 01 2010
%E More terms from _Seiichi Manyama_, Dec 22 2019
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