This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302291 #12 Apr 19 2020 12:44:09
%S A302291 1,1,2,1,3,3,3,1,4,4,2,4,4,4,4,1,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,6,6,
%T A302291 6,6,3,6,6,6,6,6,2,6,6,3,6,6,6,6,6,6,6,6,3,6,6,6,6,6,6,6,6,1,7,7,7,7,
%U A302291 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N A302291 a(n) is the period of the binary expansion of n.
%C A302291 Zero is assumed to be represented as 0; otherwise, leading zeros are ignored.
%C A302291 See A302295 for the variant where leading zeros are allowed.
%H A302291 Rémy Sigrist, <a href="/A302291/b302291.txt">Table of n, a(n) for n = 0..10000</a>
%H A302291 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A302291 a(n) = A070939(n) / A138904(n).
%F A302291 a(2^n) = n + 1 for any n >= 0.
%F A302291 a(2^n - 1) = 1 for any n >= 0.
%F A302291 a(A020330(n)) = a(n) for any n > 0.
%e A302291 The first terms, alongside the binary expansion of n with periodic part in parentheses, are:
%e A302291 n a(n) bin(n)
%e A302291 -- ---- ------
%e A302291 0 1 (0)
%e A302291 1 1 (1)
%e A302291 2 2 (10)
%e A302291 3 1 (1)(1)
%e A302291 4 3 (100)
%e A302291 5 3 (101)
%e A302291 6 3 (110)
%e A302291 7 1 (1)(1)(1)
%e A302291 8 4 (1000)
%e A302291 9 4 (1001)
%e A302291 10 2 (10)(10)
%e A302291 11 4 (1011)
%e A302291 12 4 (1100)
%e A302291 13 4 (1101)
%e A302291 14 4 (1110)
%e A302291 15 1 (1)(1)(1)(1)
%e A302291 16 5 (10000)
%e A302291 17 5 (10001)
%e A302291 18 5 (10010)
%e A302291 19 5 (10011)
%e A302291 20 5 (10100)
%t A302291 Table[If[n==0,1,Length[Union[Array[RotateRight[IntegerDigits[n,2],#]&,IntegerLength[n,2]]]]],{n,0,50}] (* _Gus Wiseman_, Apr 19 2020 *)
%o A302291 (PARI) a(n) = my (l=max(1, #binary(n))); fordiv (l, w, if (#Set(digits(n, 2^w))<=1, return (w)))
%Y A302291 Aperiodic compositions are counted by A000740.
%Y A302291 Aperiodic binary words are counted by A027375.
%Y A302291 The orderless period of prime indices is A052409.
%Y A302291 Numbers whose binary expansion is periodic are A121016.
%Y A302291 Periodic compositions are counted by A178472.
%Y A302291 Numbers whose prime signature is aperiodic are A329139.
%Y A302291 Compositions by number of distinct rotations are A333941.
%Y A302291 All of the following pertain to compositions in standard order (A066099):
%Y A302291 - Length is A000120.
%Y A302291 - Necklaces are A065609.
%Y A302291 - Sum is A070939.
%Y A302291 - Runs are counted by A124767.
%Y A302291 - Rotational symmetries are counted by A138904.
%Y A302291 - Strict compositions are A233564.
%Y A302291 - Constant compositions are A272919.
%Y A302291 - Lyndon compositions are A275692.
%Y A302291 - Co-Lyndon compositions are A326774.
%Y A302291 - Aperiodic compositions are A328594.
%Y A302291 - Rotational period is A333632.
%Y A302291 - Co-necklaces are A333764.
%Y A302291 - Reversed necklaces are A333943.
%Y A302291 Cf. A000031, A001037, A008965, A019536, A020330, A211100, A302295, A328595, A328596, A329312, A329313, A329326.
%K A302291 nonn,base,easy
%O A302291 0,3
%A A302291 _Rémy Sigrist_, Apr 04 2018