A226723 Positions of the numbers 3^n, for n >= 1, in the joint ranking of all the numbers 2^h, 3^k, 5^k, for h >= 0, k >= 1.

3, 7, 10, 13, 16, 20, 23, 26, 30, 32, 36, 40, 42, 46, 49, 52, 55, 59, 62, 65, 69, 72, 75, 79, 82, 85, 88, 92, 94, 98, 102, 104, 108, 111, 114, 118, 121, 124, 127, 131, 133, 137, 141, 144, 147, 150, 154, 157, 160, 164, 166, 170, 174, 176, 180, 183, 186, 189

Offset: 1

Author

Clark Kimberling, Jun 16 2013

Keywords

• nonn
• easy

Examples

			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 3^n for n >= 1 are in positions 3, 7, 10, 13, 16.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A123384, A226720, A226722, A226724, A306044.

Programs

Mathematica

z = 120; b = 2; c = 3; d = 5; f[x_]:=Floor[x];
Table[1 + n + f[n*Log[c, b]] + f[n*Log[d, b]], {n, 0, z}]  (* A226722 *)
Table[1 + n + f[n*Log[b, c]] + f[n*Log[d, c]], {n, 1, z}]  (* A226723 *)
Table[1 + n + f[n*Log[b, d]] + f[n*Log[c, d]], {n, 1, z}]  (* A226724 *)

Formula

a(n) = 1 + n + floor(n*log_2(3)) + floor(n*log_5(3)).