A305394 - OEIS

%I #34 Jun 26 2022 22:45:11

%S 5,4,5,3,5,4,5,5,4,5,3,5,4,5,4,5,3,5,4,5,5,4,5,3,5,4,5,3,5,4,5,5,4,5,

%T 3,5,4,5,4,5,3,5,4,5,5,4,5,3,5,4,5,5,4,5,3,5,4,5,4,5,3,5,4,5,5,4,5,3,

%U 5,4,5,3,5,4,5,5,4,5,3,5,4,5,4,5,3,5,4,5,5,4,5,3,5,4,5,4

%N First differences of A140103.

%C Conjecture: this sequence is the ternary tribonacci word on the alphabet {5,4,3}, i.e., (a(n)) is the unique fixed point of the  morphism 5 -> 54, 4 -> 53, 3 -> 5; see A092782. - _Michel Dekking_, Mar 13 2019

%C An equivalent conjecture: This sequence (prefixed by 3 since A140103 should really begin with 0) is 3.TTW(5,4,3) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(5,4,3), where THETA is defined in A275925. There are similar conjectures for the first differences of A140100, A140101, A140102. - _N. J. A. Sloane_, Mar 14 2019 and 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="/A305394/b305394.txt">Table of n, a(n) for n = 1..49999</a>F.

%H 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) = A140103(n+1) - A140103(n).

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 23 2018