A329990 - OEIS

%I #4 Jan 03 2020 20:20:20

%S 1,2,3,5,6,7,9,10,11,13,14,15,17,18,19,20,22,23,24,26,27,28,30,31,32,

%T 34,35,36,38,39,40,41,43,44,45,47,48,49,51,52,53,55,56,57,58,60,61,62,

%U 64,65,66,68,69,70,72,73,74,76,77,78,79,81,82,83,85,86

%N Beatty sequence for the number x satisfying 1/x + 1/3^x = 1.

%C 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.

%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), where x = 1.31056994... is the constant in A329989.

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

%t RealDigits[r][[1]] (* A329989 *)

%t Table[Floor[n*r], {n, 1, 250}]  (* A329990 *)

%t Table[Floor[n*2^r], {n, 1, 250}]  (* A329991 *)

%Y Cf. A329825, A329989, A329991 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jan 02 2020