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 A286687 #23 Jun 02 2024 08:19:02
%S A286687 2,4,5,8,10,11,14,16,18,19,22,24,25,28,30,32,33,36,38,39,42,44,45,48,
%T A286687 50,52,53,56,58,59,62,64,66,67,70,72,73,76,78,79,82,84,86,87,90,92,93,
%U A286687 96,98,100,101,104,106,107,110,112,114,115,118,120,121,124
%N A286687 Positions of 1 in A286685; complement of A286686.
%C A286687 a(n) - a(n-1) is in {1,2,3} for n >= 2, and a(n)/n -> 2.
%C A286687 These are also the positions of 0 in the {0->10, 1->01}-transform of the Pell word, A171588.
%C A286687 From _Michel Dekking_, Feb 21 2018: (Start)
%C A286687 Let tau be transform map tau: 0->01, 1->10. By definition A286685 equals tau(b), where b is the Pell word. The words of length 2 occurring in b are 00, 01 and 10. These are mapped by tau to tau(00) = 0101, tau(01) = 0110, tau(10) = 1001.
%C A286687 Each of these three four-letter words contains exactly 2 1's, occurring among the first two letters and among the last two letters. It follows from this that the overlapping words of length 2 in the Pell word b induce distances between 1's in tau(b) of 2 for 00, of 1 for 01, and of 3 for 10. But then the difference sequence (a(n+1) - a(n)) = 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 2, 2, ... is equal to the 1->2, 2->1 permuted version of the 3-symbol Pell word A294180. (End)
%H A286687 Clark Kimberling, <a href="/A286687/b286687.txt">Table of n, a(n) for n = 1..10000</a>
%e A286687 As a word, A286685 = 01011001011001010110010110..., in which 0 is in positions 1,3,6,7,9,12,...
%t A286687 s = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0}}] &, {0}, 6] (* A171588 *)
%t A286687 w = StringJoin[Map[ToString, s]]
%t A286687 w1 = StringReplace[w, {"0" -> "01", "1"->"10"}]
%t A286687 st = ToCharacterCode[w1] - 48 ; (* A286685 *)
%t A286687 Flatten[Position[st, 0]]; (* A286686 *)
%t A286687 Flatten[Position[st, 1]]; (* this sequence *)
%Y A286687 Cf. A171588, A286685, A286686.
%K A286687 nonn,easy
%O A286687 1,1
%A A286687 _Clark Kimberling_, May 13 2017