A275888 - OEIS

%I #16 Dec 08 2023 06:14:54

%S 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,

%T 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,

%U 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

%N First differences of A275884.

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

%C 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

%H Boon Suan Ho, <a href="/A275888/b275888.txt">Table of n, a(n) for n = 1..110000</a> (first 30900 terms from N. J. A. Sloane)

%H Boon Suan Ho, <a href="/A275888/a275888.txt">Observations about A275888</a>

%Y Cf. A275884.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Aug 18 2016