%I #5 Dec 14 2018 18:21:10
%S 2,4,6,9,11,13,16,18,20,22,24,27,29,31,34,36,38,40,42,45,47,49,52,54,
%T 56,59,61,63,65,67,70,72,74,77,79,81,83,85,88,90,92,95,97,99,102,104,
%U 106,108,110,113,115,117,120,122,124,126,128,131,133,135,138
%N Position of 1/2^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.
%C Every positive integer is in exactly one of the sequences A322532, A322533, A322534.
%H Clark Kimberling, <a href="/A322532/b322532.txt">Table of n, a(n) for n = 1..10000</a>
%F Position of 1/2^n: n + floor(n log(2)/log(3)) + floor((n + 1) log(2)/log(3))
%F Position of 1/3^n: 2n - 2 + floor(n log(3)/log(2))
%F Position of 2/3^n: 2n + floor(n log(3)/log(2))
%e In the decreasing sequence 2/3, 1/2, 1/3, 1/4, 2/9, 1/8, 1/9, 2/27, 1/16, ..., the positions of 1/2, 1/4, 1/8, 1/6, are 2,4,6,9; the positions of 1/3, 1/9, 1/27,... are 3,7,10,14,...; the positions of 2/3, 2/9,2/27,... are 1,5,8,12,...
%t a[n_] := n + Floor[n Log[2]/Log[3]] + Floor[(n + 1) Log[2]/Log[3]];
%t b[n_] := 2 n - 2 + Floor[n Log[3]/Log[2]];
%t c[n_] := 2 n + Floor[n Log[3]/Log[2]];
%t Table[a[n], {n, 1, 120}] (* A322532 *)
%t Table[b[n], {n, 1, 120}] (* A322533 *)
%t Table[c[n], {n, 1, 120}] (* A322534 *)
%Y Cf. A322533, A322534.
%K nonn
%O 1,1
%A _Clark Kimberling_, Dec 14 2018