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A302295 a(n) is the period of the binary expansion of n (with leading zeros allowed).

%I A302295 #8 Apr 07 2018 03:56:39
%S A302295 1,1,2,1,3,2,3,1,4,3,2,4,4,4,4,1,5,4,3,5,5,2,5,5,5,5,5,3,5,5,5,1,6,5,
%T A302295 4,6,3,6,6,6,6,6,2,6,6,3,6,6,6,6,6,4,6,6,3,6,6,6,6,6,6,6,6,1,7,6,5,7,
%U A302295 4,7,7,7,7,3,7,7,7,7,7,7,7,7,7,7,7,2,7
%N A302295 a(n) is the period of the binary expansion of n (with leading zeros allowed).
%C A302295 Equivalently, a(n) is the least positive k such that n is a repdigit number in base 2^k.
%C A302295 See A302291 for the variant where leading zeros are not allowed.
%H A302295 Rémy Sigrist, <a href="/A302295/b302295.txt">Table of n, a(n) for n = 0..10000</a>
%H A302295 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A302295 a(2^n) = n + 1 for any n >= 0.
%F A302295 a(2^n - 1) = 1 for any n >= 0.
%F A302295 a(n) <= A302291(n).
%F A302295 A059711(n) <= 2^a(n).
%e A302295 The first terms, alongside the binary expansion of n with periodic part in parentheses, are:
%e A302295   n  a(n)    bin(n)
%e A302295   -- ----    ------
%e A302295    0    1    (0)
%e A302295    1    1    (1)
%e A302295    2    2    (10)
%e A302295    3    1    (1)(1)
%e A302295    4    3    (100)
%e A302295    5    2    (01)(01)
%e A302295    6    3    (110)
%e A302295    7    1    (1)(1)(1)
%e A302295    8    4    (1000)
%e A302295    9    3    (001)(001)
%e A302295   10    2    (10)(10)
%e A302295   11    4    (1011)
%e A302295   12    4    (1100)
%e A302295   13    4    (1101)
%e A302295   14    4    (1110)
%e A302295   15    1    (1)(1)(1)(1)
%e A302295   16    5    (10000)
%e A302295   17    4    (0001)(0001)
%e A302295   18    3    (10)(10)
%e A302295   19    5    (10011)
%e A302295   20    5    (10100)
%o A302295 (PARI) a(n) = for (k=1, oo, if (#Set(digits(n, 2^k))<=1, return (k)))
%Y A302295 Cf. A059711, A302291.
%K A302295 nonn,base,easy
%O A302295 0,3
%A A302295 _Rémy Sigrist_, Apr 04 2018