A206805 Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.

1, 3, 4, 6, 8, 9, 11, 13, 14, 16, 17, 19, 21, 22, 24, 26, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 79, 81, 83, 84, 86, 88, 89, 91, 92, 94, 96, 97, 99, 101, 102, 104, 106, 107

Offset

1,2

Comments

The joint ranking is for j >= 1 and k >= 1, so that the sets {2^j} and {3^k} are disjoint. Not identical to A182774; e.g., A206805 contains 318 but A182774 does not.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Formula

a(n) = n + floor(n*log_2(3)) (while A206807(n) = n + floor(n*log_3(2))).

Example

The joint ranking begins with 2,3,4,8,9,16,27,32,64,81,128,243,256, so that
this sequence = (1,3,4,6,8,9,11,13,...),
A206807       = (2,5,7,10,12,...).

Mathematica

f[n_] := 2^n; g[n_] := 3^n; z = 200;
c = Table[f[n], {n, 1, z}]; s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]]; q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]] (* A206805 *)
Table[n + Floor[n*Log[3, 2]], {n, 1, 50}] (* A206805 *)
Flatten[Table[q[n], {n, 1, z}]]  (* A206807 *)
Table[n + Floor[n*Log[2, 3]], {n, 1, 50}] (* A206807 *)

Prog

(PARI) a(n) = n + floor(n*log(2)/log(3)); \\ Jinyuan Wang, Jan 27 2020

Crossrefs

Cf. A182773, A182774, A206807.

Sequence in context: A188035 A026339 A182774 * A109259 A292663 A182772

Adjacent sequences: A206802 A206803 A206804 * A206806 A206807 A206808

Keyword

nonn

Author

Clark Kimberling, Feb 16 2012

Status

approved