A211096 Smallest (i.e., rightmost) Lyndon word in the Lyndon factorization of the binary representation of n (written using 1's and 2's rather than 0's and 1's, since numbers > 0 in the OEIS cannot begin with 0).

1, 2, 1, 2, 1, 12, 1, 2, 1, 112, 1, 122, 1, 12, 1, 2, 1, 1112, 1, 1122, 1, 12, 1, 1222, 1, 112, 1, 122, 1, 12, 1, 2, 1, 11112, 1, 11122, 1, 11212, 1, 11222, 1, 112, 1, 12122, 1, 12, 1, 12222, 1, 1112, 1, 1122, 1, 12, 1, 1222, 1, 112, 1, 122, 1, 12, 1, 2, 1, 111112, 1, 111122, 1, 111212, 1, 111222, 1, 112, 1, 112122, 1, 112212, 1, 112222, 1, 1112, 1, 1122, 1

Offset: 0

Author

N. J. A. Sloane, Mar 31 2012

Keywords

• nonn

Comments

See A211095 and A211097 for further information, including Maple programs.

Examples

			n=25 has binary expansion 11001, which has Lyndon factorization (1)(1)(001) with three factors. The rightmost factor is 001, which we write as a(25) = 112.
The real sequence (written with 0's and 1's rather than 1's and 2's) is:
0, 1, 0, 1, 0, 01, 0, 1, 0, 001, 0, 011, 0, 01, 0, 1, 0, 0001, 0, 0011, 0, 01, 0, 0111, 0, 001, 0, 011, 0, 01, 0, 1, 0, 00001, 0, 00011, 0, 00101, 0, 00111, 0, 001, 0, 01011, 0, 01, 0, 01111, 0, 0001, 0, 0011, 0, 01, 0, 0111, 0, 001, 0, 011, ...
		

Crossrefs

Cf. A211100, A211095, A211097, A211098, A211099.

Formula

a(2k) is always 1 (i.e., 0).