A211096 - OEIS

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

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OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..84.

FORMULA

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

EXAMPLE

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.

Sequence in context: A126906 A179508 A134304 * A134569 A295853 A287541

Adjacent sequences: A211093 A211094 A211095 * A211097 A211098 A211099

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 31 2012

STATUS

approved