A330094 Beatty sequence for 2^x, where 1/2^x + 1/3^(x-1) = 1.

2, 5, 8, 10, 13, 16, 18, 21, 24, 26, 29, 32, 34, 37, 40, 42, 45, 48, 50, 53, 56, 59, 61, 64, 67, 69, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 99, 101, 104, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, 134, 136, 139, 142, 144, 147, 150, 152, 155, 158, 161

Offset

1,1

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..60.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*2^x), 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, A330093, A330095 (complement).

Sequence in context: A047618 A236535 A059551 * A189535 A330214 A182769

Adjacent sequences: A330091 A330092 A330093 * A330095 A330096 A330097

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved