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A211095
Length of the smallest (i.e., rightmost) Lyndon word in the Lyndon factorization of the binary representation of n.
6
1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 1, 4, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 1, 1, 5, 1, 5, 1, 5, 1, 5, 1, 3, 1, 5, 1, 2, 1, 5, 1, 4, 1, 4, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 1, 1, 6, 1, 6, 1, 6, 1, 6, 1, 3, 1, 6, 1, 6, 1, 6, 1, 4, 1, 4, 1, 2, 1, 6, 1, 3, 1, 3, 1, 2, 1, 6, 1, 5, 1, 5, 1, 5, 1, 5, 1, 3, 1, 5, 1, 2, 1, 5, 1, 4, 1, 4, 1, 2, 1, 4, 1
OFFSET
0,6
COMMENTS
See A211100 for more details.
The length of the largest (or leftmost) Lyndon word in the factorization is always 1.
FORMULA
a(2k) = 1 always (the only Lyndon word ending in 0 is 0 itself).
EXAMPLE
n=25 has binary expansion 11001, which has Lyndon factorization (1)(1)(001) with three factors. The rightmost factor, 001, has length 3, so a(25)=3.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 31 2012
STATUS
approved