A226722 Positions of the numbers 2^n, for n >=0, in the joint ranking of all the numbers 2^h, 3^k, 5^k, for h >= 0, k >= 1.

1, 2, 4, 6, 8, 11, 12, 15, 17, 18, 21, 22, 25, 27, 29, 31, 33, 35, 37, 39, 41, 44, 45, 47, 50, 51, 54, 56, 58, 60, 61, 64, 66, 68, 70, 73, 74, 76, 78, 80, 83, 84, 87, 89, 90, 93, 95, 97, 99, 101, 103, 105, 107, 109, 112, 113, 116, 117, 119, 122, 123, 126

Offset

1,2

Links

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

Formula

a(n) = 1 + n + floor(n*log_3(2)) + floor(n*log_5(2).

Example

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 2^n for n >= 0 are in positions 1, 2, 4, 6, 8, 11, 12, 15, 17, 18.

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 *)

Crossrefs

Cf. A123384, A226720, A226723, A226724, A306044.

Sequence in context: A256342 A171820 A193879 * A187414 A187348 A081499

Adjacent sequences: A226719 A226720 A226721 * A226723 A226724 A226725

Keyword

nonn,easy

Author

Clark Kimberling, Jun 16 2013

Status

approved