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0, 1, 4, 5, 6, 7, 8, 9, 12, 13, 16, 17, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 44, 45, 48, 49, 52, 53, 54, 55, 56, 57, 60, 61, 64, 65, 68, 69, 70, 71, 72, 73, 76, 77, 80, 81, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 104
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OFFSET
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1,3
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COMMENTS
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Locates patterns of the form 0x1 or 1x0 in the Thue-Morse sequence.
The asymptotic density of this sequence is 2/3 (Rowland and Yassawi, 2015; Burns, 2016). - Amiram Eldar, Jan 30 2021
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LINKS
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MATHEMATICA
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tm[0] = 0; tm[n_?EvenQ] := tm[n] = tm[n/2]; tm[n_] := tm[n] = 1 - tm[(n - 1)/2]; Reap[For[n = 0, n <= 6000, n++, If[tm[n] + tm[n + 2] == 1, Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)
Flatten[Position[Partition[ThueMorse[Range[0, 120]], 3, 1], _?(#[[1]]+#[[3]] == 1&), 1, Heads->False]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2019 *)
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PROG
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CROSSREFS
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Cf. A161673, A161639, A161641, A161627, A161579, A161580, A161890, A121539, A131323, A036554, A010060, A079523, A081706.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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