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A305374 First differences of A140101.

%I A305374 #40 Mar 07 2020 13:50:20
%S A305374 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 A305374 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 A305374 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 A305374 First differences of A140101.
%C A305374 Or, prefix A276788 with a 1 and then add 1 to every term.
%C A305374 This relation between A003144 and A140101 is a conjecture (Daniel Forgues remarks would trivially follow from this relation). - _Michel Dekking_, Mar 18 2019
%C A305374 The lengths of the successive runs of 3's are given by A275925.
%C A305374 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 A305374 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 A305374 All these conjectures are now theorems - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019
%H A305374 N. J. A. Sloane, <a href="/A305374/b305374.txt">Table of n, a(n) for n = 0..49999</a>
%H A305374 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 A305374 a(n) = A140101(n+1)-A140101(n).
%Y A305374 Cf. A003144, A140101, A275925, A276788.
%Y A305374 For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.
%K A305374 nonn
%O A305374 0,1
%A A305374 _N. J. A. Sloane_, Jun 09 2018