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 A334265 #13 Apr 25 2020 08:40:24
%S A334265 0,1,2,4,5,8,9,11,16,17,18,19,21,23,32,33,34,35,37,39,41,43,47,64,65,
%T A334265 66,67,68,69,71,73,74,75,77,79,81,83,85,87,91,95,128,129,130,131,132,
%U A334265 133,135,137,138,139,141,143,145,146,147,149,151,155,159,161,163
%N A334265 Numbers k such that the k-th composition in standard order is a reversed Lyndon word.
%C A334265 Reversed Lyndon words are different from co-Lyndon words (A326774).
%C A334265 A Lyndon word is a finite sequence of positive integers that is lexicographically strictly less than all of its cyclic rotations.
%C A334265 The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
%e A334265 The sequence of all reversed Lyndon words begins:
%e A334265 0: () 37: (3,2,1) 83: (2,3,1,1)
%e A334265 1: (1) 39: (3,1,1,1) 85: (2,2,2,1)
%e A334265 2: (2) 41: (2,3,1) 87: (2,2,1,1,1)
%e A334265 4: (3) 43: (2,2,1,1) 91: (2,1,2,1,1)
%e A334265 5: (2,1) 47: (2,1,1,1,1) 95: (2,1,1,1,1,1)
%e A334265 8: (4) 64: (7) 128: (8)
%e A334265 9: (3,1) 65: (6,1) 129: (7,1)
%e A334265 11: (2,1,1) 66: (5,2) 130: (6,2)
%e A334265 16: (5) 67: (5,1,1) 131: (6,1,1)
%e A334265 17: (4,1) 68: (4,3) 132: (5,3)
%e A334265 18: (3,2) 69: (4,2,1) 133: (5,2,1)
%e A334265 19: (3,1,1) 71: (4,1,1,1) 135: (5,1,1,1)
%e A334265 21: (2,2,1) 73: (3,3,1) 137: (4,3,1)
%e A334265 23: (2,1,1,1) 74: (3,2,2) 138: (4,2,2)
%e A334265 32: (6) 75: (3,2,1,1) 139: (4,2,1,1)
%e A334265 33: (5,1) 77: (3,1,2,1) 141: (4,1,2,1)
%e A334265 34: (4,2) 79: (3,1,1,1,1) 143: (4,1,1,1,1)
%e A334265 35: (4,1,1) 81: (2,4,1) 145: (3,4,1)
%t A334265 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A334265 lynQ[q_]:=Length[q]==0||Array[Union[{q,RotateRight[q,#1]}]=={q,RotateRight[q,#1]}&,Length[q]-1,1,And];
%t A334265 Select[Range[0,100],lynQ[Reverse[stc[#]]]&]
%Y A334265 The non-reversed version is A275692.
%Y A334265 The generalization to necklaces is A333943.
%Y A334265 The dual version (reversed co-Lyndon words) is A328596.
%Y A334265 The case that is also co-Lyndon is A334266.
%Y A334265 Binary Lyndon words are counted by A001037.
%Y A334265 Lyndon compositions are counted by A059966.
%Y A334265 Normal Lyndon words are counted by A060223.
%Y A334265 Numbers whose prime signature is a reversed Lyndon word are A334298.
%Y A334265 All of the following pertain to compositions in standard order (A066099):
%Y A334265 - Length is A000120.
%Y A334265 - Necklaces are A065609.
%Y A334265 - Sum is A070939.
%Y A334265 - Reverse is A228351 (triangle).
%Y A334265 - Strict compositions are A233564.
%Y A334265 - Constant compositions are A272919.
%Y A334265 - Lyndon words are A275692.
%Y A334265 - Reversed Lyndon words are A334265 (this sequence).
%Y A334265 - Co-Lyndon words are A326774.
%Y A334265 - Reversed co-Lyndon words are A328596.
%Y A334265 - Length of Lyndon factorization is A329312.
%Y A334265 - Distinct rotations are counted by A333632.
%Y A334265 - Lyndon factorizations are counted by A333940.
%Y A334265 - Length of Lyndon factorization of reverse is A334297.
%Y A334265 Cf. A000031, A027375, A138904, A211100, A328595, A329131, A329313, A333764, A334028, A334267.
%K A334265 nonn
%O A334265 1,3
%A A334265 _Gus Wiseman_, Apr 22 2020