

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: nonattacking 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



