A322533 - OEIS

%I #5 Dec 14 2018 18:21:17

%S 3,7,10,14,17,21,25,28,32,35,39,43,46,50,53,57,60,64,68,71,75,78,82,

%T 86,89,93,96,100,103,107,111,114,118,121,125,129,132,136,139,143,146,

%U 150,154,157,161,164,168,172,175,179,182,186,190,193,197,200,204

%N Position of 1/3^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="/A322533/b322533.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. A322532, A322534.

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 14 2018