A226724 - OEIS

%I #15 Nov 02 2024 18:00:46

%S 5,9,14,19,24,28,34,38,43,48,53,57,63,67,71,77,81,86,91,96,100,106,

%T 110,115,120,125,129,135,139,143,148,153,158,162,168,172,177,182,187,

%U 191,197,201,205,211,215,220,225,230,234,240,244,249,254,259,263,269

%N Positions of the numbers 5^n, for n >= 1, in the joint ranking of all the numbers 2^h, 3^k, 5^k, for h >= 0, k >= 1.

%H Clark Kimberling, <a href="/A226724/b226724.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = 1 + n + floor(n*log_2(5)) + floor(n*log_3(5)).

%e The joint ranking of the powers of 2, 3, 5 begins like this: 1, 2, 3, 4, 5, 8, 9, 16, 25, 27, 32, 64, 81, 125, 128, 243, 256, 512.  The numbers 5^n for n >= 0 are in positions 5, 9, 14.

%t z = 120; b = 2; c = 3; d = 5; f[x_]:=Floor[x];

%t Table[1 + n + f[n*Log[c, b]] + f[n*Log[d, b]], {n, 0, z}]  (* A226722 *)

%t Table[1 + n + f[n*Log[b, c]] + f[n*Log[d, c]], {n, 1, z}]  (* A226723 *)

%t Table[1 + n + f[n*Log[b, d]] + f[n*Log[c, d]], {n, 1, z}]  (* A226724 *)

%Y Cf. A123384, A226720, A226722, A226723, A306044.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 16 2013