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0, 2, 3, 4, 6, 7, 9, 13, 15, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 32, 34, 35, 36, 38, 39, 41, 45, 47, 48, 50, 51, 52, 54, 55, 57, 61, 63, 64, 66, 67, 68, 70, 71, 73, 77, 79, 80, 82, 83, 84, 86, 88, 90, 91, 92, 94, 96, 98, 99, 100, 102, 103, 105, 109, 111, 112, 114, 115, 116, 118, 120
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OFFSET
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0,2
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COMMENTS
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Or union of intersection of A161639 and {A079523(n)-8} and intersection of A161673 and {A121539(n)-8}. In general, for a>=1, consider equations A010060(x+a)+A010060(x)=1, A010060(x+a)=A010060(x). Denote via B_a (C_a) the sequence of nonnegative solutions of the first (second) equation. Then we have recursions: B_(a+1) is the union of transactions 1) C_a and {A121539(n)-a}, 2) B_a and {A079523(n)-a}; C_(a+1) is the union of transactions 1) C_a and {A079523(n)-a}, 2) B_a and {A121539(n)-a}.
This conjecture was actually proved in a later version of the Shevelev arxiv article cited below, and it can also easily be proved by the Walnut prover. - Jeffrey Shallit, Oct 12 2022
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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 <= 18000, n++, If[tm[n] == tm[n + 9], Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)
SequencePosition[ThueMorse[Range[0, 150]], {x_, _, _, _, _, _, _, _, _, x_}][[All, 1]]-1 (* Harvey P. Dale, Feb 06 2023 *)
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PROG
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CROSSREFS
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Cf. A161824, A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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