A339608 Numbers whose bijective base-2 representation is a Lyndon word.
1, 2, 4, 8, 10, 16, 18, 22, 32, 34, 36, 38, 42, 46, 64, 66, 68, 70, 74, 76, 78, 86, 94, 128, 130, 132, 134, 136, 138, 140, 142, 146, 148, 150, 154, 156, 158, 170, 174, 182, 190, 256, 258, 260, 262, 264, 266, 268, 270, 274, 276, 278, 280, 282, 284, 286, 292, 294, 298, 300, 302, 308
Offset: 1
Examples
1 and 2 are in this sequence, since their bijective base-2 representations are also just "1" and "2", and words of just one letter have no nontrivial rotations. 3 is not in this sequence, since written in bijective base-2 it becomes "11", which is equal to its single nontrivial rotation. 108 is not in this sequence, since in bijective base-2 it becomes "212212", which is larger than two of its nontrivial rotations (both equal to "122122"). However, "212212" can be uniquely split into the lexicographically nonincreasing sequence of Lyndon words "2", "122" and "12", corresponding to 2, 10 and 4 in this sequence.
Links
- Harald Korneliussen, Table of n, a(n) for n = 1..20000
- Wikipedia, Bijective numeration
- Wikipedia, Standard factorization of a Lyndon word
Formula
Observation: a(n) = 2*A326774(n-1), n >= 2. (At least for the terms from the Data section). - Omar E. Pol, Dec 09 2020
a(n) = A329327(n) - 1. - Harald Korneliussen, Mar 02 2021
Comments