A330144 Beatty sequence for (5/2)^x, where (3/2)^x + (5/2)^x = 1.

2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 46, 49, 52, 55, 57, 60, 63, 66, 69, 71, 74, 77, 80, 82, 85, 88, 91, 93, 96, 99, 102, 104, 107, 110, 113, 115, 118, 121, 124, 127, 129, 132, 135, 138, 140, 143, 146, 149, 151, 154, 157, 160, 162

Offset

1,1

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..59.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n (5/2)^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, A330143 (complement).

Sequence in context: A007826 A108589 A292988 * A187341 A329924 A330112

Adjacent sequences: A330141 A330142 A330143 * A330145 A330146 A330147

Keyword

nonn,easy

Author

Clark Kimberling, Jan 04 2020

Status

approved