This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305393 #26 Mar 07 2020 13:50:20 %S A305393 1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,1,2,1,1,2,1, %T A305393 1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1, %U A305393 1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1 %N A305393 First differences of A140102. %C A305393 Although initially this agrees with A293630, the sequences are distinct. %C A305393 From _Michel Dekking_, Mar 18 2019: (Start) %C A305393 Let x be the tribonacci word x = A092782 = 1,2,1,3,1,2,1,1,... %C A305393 Consider the morphism delta: %C A305393 1 -> 1112, %C A305393 2 -> 112, %C A305393 3 -> 12. %C A305393 Conjecture: (a(n)) = 12 delta(x). %C A305393 (End) %C A305393 Conjecture: This sequence (prefixed by 1 since A140102 should really begin with 0) is 1.TTW(1,2,1) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(1,2,1), where THETA is defined in A275925. - _N. J. A. Sloane_, Mar 19 2019 %C A305393 All these conjectures are now theorems - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019 %H A305393 N. J. A. Sloane, <a href="/A305393/b305393.txt">Table of n, a(n) for n = 1..49999</a> %H A305393 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 A305393 a(n) = A140102(n+1)-A140102(n), n >= 1. %Y A305393 For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394. %Y A305393 Cf. A293630. %K A305393 nonn %O A305393 1,2 %A A305393 _N. J. A. Sloane_, Jun 23 2018