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%I #8 Mar 02 2020 19:28:13
%S 6,10,18,24,30,34,40,46,54,58,66,72,78,86,90,96,102,106,114,120,126,
%T 130,136,142,150,154,160,166,170,178,184,190,198,202,210,216,222,226,
%U 232,238,246,250,258,264,270,278,282,288,294,298,306,312,318,326,330
%N Positions of 0,0 in the Thue-Morse sequence (A010060).
%C Every positive integer lies in exactly one of these four sequences: A248056, A091855, A091855, A248057.
%H Clark Kimberling, <a href="/A248056/b248056.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 2*A091785(n) for n >= 1.
%e Thue-Morse sequence: 0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,..., so that a(1) = 6 and a(2) = 10.
%t z = 400; u = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* A010060 *)
%t v = Rest[u]
%t t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
%t t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
%t Flatten[Position[t1, 1]] (* A248056 *)
%t Flatten[Position[t2, 1]] (* A091855 *)
%t Flatten[Position[t3, 1]] (* A091785 *)
%t Flatten[Position[t4, 1]] (* A248057 *)
%t SequencePosition[ThueMorse[Range[400]],{0,0}][[All,2]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 02 2020 *)
%Y Cf. A010060, A091855, A091785, A248057.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 30 2014
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