A329991 Beatty sequence for 3^x, where 1/x + 1/3^x = 1.

2, 4, 7, 9, 12, 14, 17, 19, 22, 24, 27, 29, 32, 34, 37, 39, 42, 44, 47, 49, 52, 54, 57, 59, 62, 64, 66, 69, 71, 74, 76, 79, 81, 84, 86, 89, 91, 94, 96, 99, 101, 104, 106, 109, 111, 114, 116, 119, 121, 124, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148

Offset

1,1

Comments

Let x be the solution of 1/x + 1/3^x = 1. Then (floor(n x)) and (floor(n 3^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..60.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x), where x = 1.31056994... is the constant in A329989.

Mathematica

r = x /. FindRoot[1/x + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329989 *)
Table[Floor[n*r], {n, 1, 250}]    (* A329990 *)
Table[Floor[n*2^r], {n, 1, 250}]  (* A329991 *)

Crossrefs

Cf. A329825, A329989, A329990 (complement).

Sequence in context: A064995 A329846 A067839 * A047211 A225000 A189677

Adjacent sequences: A329988 A329989 A329990 * A329992 A329993 A329994

Keyword

nonn,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved