A329996 - OEIS

%I #4 Jan 04 2020 12:56:02

%S 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,

%T 36,38,39,40,42,43,45,46,47,49,50,52,53,55,56,57,59,60,62,63,64,66,67,

%U 69,70,71,73,74,76,77,79,80,81,83,84,86,87,88,90,91,93

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

%C 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

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

%t r = x /. FindRoot[1/x^3 + 1/3^x == 1, {x, 1, 10}, WorkingPrecision -> 120]

%t RealDigits[r][[1]] (* A329995 *)

%t Table[Floor[n*r^3], {n, 1, 250}]  (* A329996 *)

%t Table[Floor[n*3^r], {n, 1, 250}]  (* A329997 *)

%Y Cf. A329825, A329995, A329997 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jan 03 2020