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%I #18 Aug 29 2018 06:32:18
%S 1,5,7,13,17,23,29,31,37,49,55,61,65,71,77,95,101,113,119,125,127,133,
%T 145,151,157,193,199,205,223,229,241,247,253,257,263,269,287,293,305,
%U 311,317,383,389,401,407,413,449,455,461,479,485,497,503,509,511,517,529
%N Positions of 1's in A317542, the formal inverse of the period-doubling sequence A096268.
%H N. Rampersad and M. Stipulanti, <a href="https://arxiv.org/abs/1807.11899">The Formal Inverse of the Period-Doubling Sequence</a>, arXiv preprint arXiv:1807.11899 [math.CO], 2018.
%t a[0] = 1;
%t a[n_] :=
%t Module[{m, u, i},
%t u[0] = 0; u[1] = 1; u[2] = 0; u[3] = 0;
%t u[i_] := If[EvenQ[i], 0, If[IntegerQ[(i - 1)/4], u[2 ((i - 1)/4) - 1], u[(i - 3)/4]]];
%t m = a[n - 1] + 1;
%t While[u[m] == 0, m++];
%t m
%t ]
%Y Cf. A096268, A317542, A317544.
%K nonn
%O 0,2
%A _Manon Stipulanti_, Jul 30 2018
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