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A275888
First differences of A275884.
2
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)
CROSSREFS
Cf. A275884.
Sequence in context: A363085 A359577 A030401 * A308166 A295931 A295920
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 18 2016
STATUS
approved