A330095 Beatty sequence for 3^(x-1), where 1/2^x + 1/3^(x-1) = 1.

1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 19, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 70, 71, 73, 74, 76, 78, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 98, 100, 102, 103

Offset

1,2

Comments

Let x be the solution of 1/2^x + 1/3^(x-1) = 1. Then (floor(n 2^x) and (floor(n 3^(x-1))) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.

Links

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n 3^(x-1)), where x = 1.4243198392... is the constant in A330093.

Mathematica

r = x /. FindRoot[1/2^x + 1/3^(x - 1) == 1, {x, 1, 10}, WorkingPrecision -> 200]
RealDigits[r][[1]] (* A330093 *)
Table[Floor[n*2^r], {n, 1, 250}]  (* A330094 *)
Table[Floor[n*3^(r - 1)], {n, 1, 250}]  (* A330095 *)

Crossrefs

Cf. A329825, A330094, A330095 (complement).

Sequence in context: A056576 A182770 A347792 * A059552 A047516 A247425

Adjacent sequences: A330092 A330093 A330094 * A330096 A330097 A330098

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved