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

0,6

Comments

See A211100 for more details.

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

Links

Table of n, a(n) for n=0..120.

N. J. A. Sloane, Maple programs

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

Cf. A211100, A211096-A211099.

Sequence in context: A356958 A057043 A325307 * A070091 A091981 A060247

Adjacent sequences: A211092 A211093 A211094 * A211096 A211097 A211098

Keyword

nonn

Author

N. J. A. Sloane, Mar 31 2012

Status

approved