A329996 Beatty sequence for x^3, where 1/x^3 + 1/3^x = 1.

1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 79, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93

Offset

1,2

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..66.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(n x^3), 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, A329997 (complement).

Sequence in context: A288204 A047381 A286428 * A258833 A097506 A189794

Adjacent sequences: A329993 A329994 A329995 * A329997 A329998 A329999

Keyword

nonn,easy

Author

Clark Kimberling, Jan 03 2020

Status

approved