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A286989 Positions of 1 in A286987; complement of A286988.

%I A286989 #7 May 21 2017 14:30:51
%S A286989 1,2,4,5,7,9,10,12,14,15,17,18,20,22,23,25,27,28,30,31,33,35,36,38,40,
%T A286989 41,43,45,46,48,49,51,53,54,56,58,59,61,62,64,66,67,69,71,72,74,76,77,
%U A286989 79,80,82,84,85,87,89,90,92,93,95,97,98,100,102,103,105
%N A286989 Positions of 1 in A286987; complement of A286988.
%C A286989 a(n) - a(n-1) is in {1,2} for n>=2, and a(n)/n -> (10 + sqrt(2))/7.
%C A286989 Is this the union of {1} and A226720? - _R. J. Mathar_, May 21 2017
%H A286989 Clark Kimberling, <a href="/A286989/b286989.txt">Table of n, a(n) for n = 1..10000</a>
%e A286989 As a word, A286987 = 1101101011010110110101..., in which 1 is in positions 1,2,4,5,7,9,....
%t A286989 s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 11]; (* Sturmian word A080764 *)
%t A286989 w = StringJoin[Map[ToString, s]];
%t A286989 w1 = StringReplace[w, {"111" -> "1"}]
%t A286989 st = ToCharacterCode[w1] - 48 ; (* A286987 *)
%t A286989 Flatten[Position[st, 0]];  (* A286988 *)
%t A286989 Flatten[Position[st, 1]];  (* A286989 *)
%Y A286989 Cf. A080764, A286987, A286988.
%K A286989 nonn,easy
%O A286989 1,2
%A A286989 _Clark Kimberling_, May 19 2017