A305393 First differences of A140102.

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

Offset: 1

Author

N. J. A. Sloane, Jun 23 2018

Keywords

• nonn

Comments

Although initially this agrees with A293630, the sequences are distinct.

From Michel Dekking, Mar 18 2019: (Start)

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

Consider the morphism delta:

1 -> 1112,

2 -> 112,

3 -> 12.

Conjecture: (a(n)) = 12 delta(x).

(End)

Conjecture: This sequence (prefixed by 1 since A140102 should really begin with 0) is 1.TTW(1,2,1) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(1,2,1), 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.

Cf. A293630.

Formula

a(n) = A140102(n+1)-A140102(n), n >= 1.