A305374 - OEIS

%I #40 Mar 07 2020 13:50:20

%S 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,

%T 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,

%U 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

%N First differences of A140101.

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

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

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

%C 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

%C 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

%C All these conjectures are now theorems - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019

%H N. J. A. Sloane, <a href="/A305374/b305374.txt">Table of n, a(n) for n = 0..49999</a>

%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.

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

%Y Cf. A003144, A140101, A275925, A276788.

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

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Jun 09 2018