A275888 First differences of A275884.

1, 1, 3, 1, 1, 1, 3, 2, 2, 1, 1, 1, 3, 1, 1, 1, 3, 2, 2, 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 1, 2, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 3, 2, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 1, 2, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1, 3, 2, 2, 1, 1, 2, 1, 2

Offset

1,3

Comments

Weak conjecture: a(n) <= 4. Does a 5 ever appear?

Suppose we think of (a(n)) as a sequence of words, each with exactly one 3, that 3 being at the end. Then, it becomes 113, 1113, 221113, 1113, 221211223, .... Empirical evidence suggests that there are exactly 156 possible words. These words range in length from 2 to 26, and all of them appear by n = 109000, with no new words showing up between n = 109000 and n = 618033989. Five of these 156 words contain a 4, and 63 of these words are faithful in the sense that they are always followed by a specific word, at least up to n = 618033989. For details, see "Observations about A275888" in the links below. - Boon Suan Ho, Oct 31 2023

Links

Boon Suan Ho, Table of n, a(n) for n = 1..110000 (first 30900 terms from N. J. A. Sloane)

Boon Suan Ho, Observations about A275888

Crossrefs

Cf. A275884.

Sequence in context: A363085 A359577 A030401 * A308166 A295931 A295920

Adjacent sequences: A275885 A275886 A275887 * A275889 A275890 A275891

Keyword

nonn

Author

N. J. A. Sloane, Aug 18 2016

Status

approved