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A248105 Positions of 1,0,1 in the Thue-Morse sequence (A010060).

%I A248105 #5 Oct 02 2014 22:36:07
%S A248105 3,12,15,20,27,36,43,48,51,60,63,68,75,80,83,92,99,108,111,116,123,
%T A248105 132,139,144,147,156,163,172,175,180,187,192,195,204,207,212,219,228,
%U A248105 235,240,243,252,255,260,267,272,275,284,291,300,303,308,315,320,323
%N A248105 Positions of 1,0,1 in the Thue-Morse sequence (A010060).
%C A248105 Every positive integer lies in exactly one of these six sequences:
%C A248105 A248056 (positions of 0,0,1)
%C A248105 A248104 (positions of 0,1,0)
%C A248105 A157970 (positions of 1,0,0)
%C A248105 A157971 (positions of 0,1,1)
%C A248105 A248105 (positions of 1,0,1)
%C A248105 A248057 (positions of 1,1,0)
%H A248105 Clark Kimberling, <a href="/A248105/b248105.txt">Table of n, a(n) for n = 1..1000</a>
%e A248105 Thue-Morse sequence:  0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,..., so that a(1) = 3 and a(2) = 12.
%t A248105 z = 600; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 13]; v = Rest[u]; w = Rest[v]; t1 = Table[If[u[[n]] == 0 && v[[n]] == 0 && w[[n]] == 1, 1, 0], {n, 1, z}];
%t A248105 t2 = Table[If[u[[n]] == 0 && v[[n]] == 1 && w[[n]] == 0, 1, 0], {n, 1, z}];
%t A248105 t3 = Table[If[u[[n]] == 1 && v[[n]] == 0 && w[[n]] == 0, 1, 0], {n, 1, z}];
%t A248105 t4 = Table[If[u[[n]] == 0 && v[[n]] == 1 && w[[n]] == 1, 1, 0], {n, 1, z}];
%t A248105 t5 = Table[If[u[[n]] == 1 && v[[n]] == 0 && w[[n]] == 1, 1, 0], {n, 1, z}];
%t A248105 t6 = Table[If[u[[n]] == 1 && v[[n]] == 1 && w[[n]] == 0, 1, 0], {n, 1, z}];
%t A248105 Flatten[Position[t1, 1]]  (* A248056 *)
%t A248105 Flatten[Position[t2, 1]]  (* A248104 *)
%t A248105 Flatten[Position[t3, 1]]  (* A157970 *)
%t A248105 Flatten[Position[t4, 1]]  (* A157971 *)
%t A248105 Flatten[Position[t5, 1]]  (* A248105 *)
%t A248105 Flatten[Position[t6, 1]]  (* A248057 *)
%Y A248105 Cf. A010060, A248056, A157970, A157971, A248104, A248057.
%K A248105 nonn,easy
%O A248105 1,1
%A A248105 _Clark Kimberling_, Oct 01 2014