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

Author

N. J. A. Sloane, Aug 18 2016

Keywords

• nonn

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.