A305374 First differences of A140101.

2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3

Offset

0,1

Comments

Or, prefix A276788 with a 1 and then add 1 to every term.

This relation between A003144 and A140101 is a conjecture (Daniel Forgues remarks would trivially follow from this relation). - Michel Dekking, Mar 18 2019

The lengths of the successive runs of 3's are given by A275925.

a(n) seems to take only the values 2 or 3, where {a(n), a(n+1)} may be {3, 2} or {2, 3} or {3, 3}, but not {2, 2}. The second differences of A140101 (first differences of this sequence) thus seem to take only the values -1 or 0 or 1. - Daniel Forgues, Aug 19 2018

Conjecture: This sequence is 2.TTW(3,3,2) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(3,3,2), 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 = 0..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.

Formula

a(n) = A140101(n+1)-A140101(n).

Crossrefs

Cf. A003144, A140101, A275925, A276788.

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

Sequence in context: A236552 A352628 A080748 * A084966 A303432 A224748

Adjacent sequences: A305371 A305372 A305373 * A305375 A305376 A305377

Keyword

nonn

Author

N. J. A. Sloane, Jun 09 2018

Status

approved