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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). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 17:05 EDT 2021. Contains 345085 sequences. (Running on oeis4.)