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%I #17 Nov 10 2019 20:03:11
%S 1,2,1,4,7,2,5,8,11,14,1,4,7,10,13,16,19,22,25,28,31,2,5,8,11,14,17,
%T 20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,1,4,7,10,13,16,19,22,25,
%U 28,31,34,37,40,43,46,49,52,55,58,61,64,67,70,73,76,79,82,85,88,91,94,97,100,103,106,109
%N a(n) = 3n minus the largest power of 2 not exceeding 3n.
%C For odd n, a(n) is odd. For even n, a(n) = 2*a(n/2).
%C Conjecture: iterations of a() stabilize at a power of 2, or at a 2-cycle (5*2^t,7*2^t).
%H Max Alekseyev, <a href="https://mathoverflow.net/q/345666">Proof that representation 3^n s - \sum_{k=0}^{n-1} 3^{n-k-1} 2^{a_k} = 2^m exists for any s</a>. MathOverflow, 2019.
%F a(n) = A053645(3*n).
%o (PARI) { A328034(n) = 3*n - 1<<(log(3*n+.5)\log(2)); }
%K nonn
%O 1,2
%A _Max Alekseyev_, Nov 10 2019