A329997 Beatty sequence for 3^x, where 1/x^3 + 1/3^x = 1.

3, 6, 10, 13, 17, 20, 24, 27, 30, 34, 37, 41, 44, 48, 51, 54, 58, 61, 65, 68, 72, 75, 78, 82, 85, 89, 92, 96, 99, 102, 106, 109, 113, 116, 120, 123, 126, 130, 133, 137, 140, 144, 147, 150, 154, 157, 161, 164, 168, 171, 174, 178, 181, 185, 188, 192, 195, 198

Offset

1,1

Comments

Let x be the solution of 1/x^3 + 1/3^x = 1. Then (floor(n*x^3)) 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..58.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n*3^x), where x = 1.12177497... is the constant in A329995.

Mathematica

r = x /. FindRoot[1/x^3 + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]
RealDigits[r][[1]] (* A329995 *)
Table[Floor[n*r^3], {n, 1, 250}]  (* A329996 *)
Table[Floor[n*3^r], {n, 1, 250}]  (* A329997 *)

Crossrefs

Cf. A329825, A329995, A329996 (complement).

Sequence in context: A189795 A145383 A258834 * A194028 A047280 A310054

Adjacent sequences: A329994 A329995 A329996 * A329998 A329999 A330000

Keyword

nonn,easy

Author

Clark Kimberling, Jan 03 2020

Status

approved