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A305392 First differences of A140100.

%I A305392 #27 Mar 07 2020 13:50:20
%S A305392 2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,2,1,2,
%T A305392 1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,1,
%U A305392 2,1,2,1,2,1,2,2,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,1,2,1,2,1
%N A305392 First differences of A140100.
%C A305392 a(n) seems to take only the values 1 or 2, where {a(n), a(n+1)} may be {2, 1} or {1, 2} or {2, 2}, but not {1, 1}, and where {a(n), a(n+1), a(n+2), a(n+3)} may be {2, 1, 2, 1} or {1, 2, 1, 2} or {1, 2, 2, 1}, but not {2, 1, 1, 2}. The second differences of A140100 (first differences of this sequence) thus seem to take only the values -1 or 0 or 1. - _Daniel Forgues_, Aug 17 2018
%C A305392 From _Michel Dekking_, Mar 16 2019: (Start)
%C A305392 Let x be the tribonacci word x = A092782 = 1,2,1,3,1,2,1,1,...
%C A305392 Consider the morphism delta:
%C A305392       1 -> 2212121212121,
%C A305392       2 -> 22121212121,
%C A305392       3 -> 2212121.
%C A305392 Conjecture: (a(n)) =  212121 delta(x).
%C A305392 (End)
%C A305392 Conjecture: This sequence (prefixed by 1 since A140100 should really begin with 0) is 1.TTW(2,1,1) where TTW is the ternary tribonacci word defined in A080843,  or equally it is THETA(2,1,1), where THETA is defined in A275925. - _N. J. A. Sloane_, Mar 19 2019
%C A305392 All these conjectures are now theorems - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019
%H A305392 N. J. A. Sloane, <a href="/A305392/b305392.txt">Table of n, a(n) for n = 1..49999</a>
%H A305392 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 A305392 a(n) = A140100(n+1)-A140100(n).
%Y A305392 For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.
%K A305392 nonn
%O A305392 1,1
%A A305392 _N. J. A. Sloane_, Jun 23 2018