A329996 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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