A305392 First differences of A140100.

2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1

Offset: 1

Author

N. J. A. Sloane, Jun 23 2018

Keywords

• nonn

Comments

a(n) seems to take only the values 1 or 2, where {a(n), a(n+1)} may be {2, 1} or {1, 2} or {2, 2}, but not {1, 1}, and where {a(n), a(n+1), a(n+2), a(n+3)} may be {2, 1, 2, 1} or {1, 2, 1, 2} or {1, 2, 2, 1}, but not {2, 1, 1, 2}. The second differences of A140100 (first differences of this sequence) thus seem to take only the values -1 or 0 or 1. - Daniel Forgues, Aug 17 2018

From Michel Dekking, Mar 16 2019: (Start)

Let x be the tribonacci word x = A092782 = 1,2,1,3,1,2,1,1,...

Consider the morphism delta:

1 -> 2212121212121,

2 -> 22121212121,

3 -> 2212121.

Conjecture: (a(n)) = 212121 delta(x).

(End)

Conjecture: This sequence (prefixed by 1 since A140100 should really begin with 0) is 1.TTW(2,1,1) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(2,1,1), where THETA is defined in A275925. - N. J. A. Sloane, Mar 19 2019

All these conjectures are now theorems - see the Dekking et al. paper. - N. J. A. Sloane, Jul 22 2019

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..49999
• F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.

Crossrefs

For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.

Formula

a(n) = A140100(n+1)-A140100(n).