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A305374 First differences of A140101. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A096520 A236552 A080748 * A084966 A303432 A224748

Adjacent sequences:  A305371 A305372 A305373 * A305375 A305376 A305377

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 09 2018

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)