A211095 Length of the smallest (i.e., rightmost) Lyndon word in the Lyndon factorization of the binary representation of n.

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

Author

N. J. A. Sloane, Mar 31 2012

Keywords

• nonn

Comments

See A211100 for more details.

The length of the largest (or leftmost) Lyndon word in the factorization is always 1.

Examples

			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.
		

Links

• N. J. A. Sloane, Maple programs

Crossrefs

Cf. A211100, A211096-A211099.

Formula

a(2k) = 1 always (the only Lyndon word ending in 0 is 0 itself).