A330143 Beatty sequence for (3/2)^x, where (2/3)^x + (2/5)^x = 1.

1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 72, 73, 75, 76, 78, 79, 81, 83, 84, 86, 87, 89, 90, 92, 94, 95, 97, 98, 100, 101

Offset

1,2

Comments

Let x be the solution of (2/3)^x + (2/5)^x = 1. Then (floor(n*(3/2)^x)) and (floor(n*(5/2)^x)) 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*(3/2)^x), where x = 1.108702608375893... is the constant in A330142.

Mathematica

r = x /.FindRoot[(2/3)^x + (2/5)^x == 1, {x, 1, 2}, WorkingPrecision -> 200]
RealDigits[r] (* A330142 *)
Table[Floor[n*(3/2)^r], {n, 1, 250}]  (* A330143 *)
Table[Floor[n*(5/2)^r], {n, 1, 250}]  (* A330144 *)

Crossrefs

Cf. A329825, A330142, A330144 (complement).

Sequence in context: A330113 A329923 A187342 * A140758 A292987 A352719

Adjacent sequences: A330140 A330141 A330142 * A330144 A330145 A330146

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved