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2, 3, 22, 38, 342, 598, 5462, 9558, 87382, 152918, 1398102, 2446678, 22369622, 39146838
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OFFSET
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0,1
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COMMENTS
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Conjecture 1: Let m(n) be the position in A268865 corresponding to a(n). Then m(n) = (2/3)*(4^n-1), if n is even, and m(n) = (2/3)*(4^(n-1)-1) + 3*4^(n-1), if n is odd.
Conjecture 2: a(n) = 2*m(n) + 2, if n is even, and a(n) = (7*m+12)/11, if n is odd.
If Conjectures 1 and 2 are true, then we easily have for even n >= 0, m(n) == 0 (mod 10), a(n) == 2 (mod 10), while a(1) = m(1) = 3 and for odd n >= 3, m(n), a(n) == 8 (mod 10). The sequence {m(n)} begins: 0, 3, 10, 58, 170, 938, 2730, 15018, 43690, ...
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LINKS
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MATHEMATICA
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nn = 10^5; f[n_, b_] := Most@ Mod[NestWhileList[-(#1 - Mod[#1, b])/b &, n, #1 != 0 &], b]; Union@ FoldList[Max, Array[(k = 0; While[Mod[Total@ f[k, 2], 2] == ThueMorse[# + k], k++]; k) &, nn - 1, 0]] (* Michael De Vlieger, Aug 25 2022 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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