%I #4 Jan 03 2020 20:20:02
%S 1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,26,27,29,30,32,33,35,36,38,
%T 39,41,42,44,45,47,48,50,52,53,55,56,58,59,61,62,64,65,67,68,70,71,73,
%U 74,76,78,79,81,82,84,85,87,88,90,91,93,94,96,97,99,100
%N Beatty sequence for the number x satisfying 1/x + 1/2^x = 1.
%C Let x be the solution of 1/x + 1/2^x = 1. Then (floor(n x)) and (floor(n 2^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 = 1.52980838275... is the constant in A329986.
%t r = x /. FindRoot[1/x + 1/2^x == 1, {x, 1, 10}, WorkingPrecision -> 210]
%t RealDigits[r][[1]] (* A329986 *)
%t Table[Floor[n*r], {n, 1, 250}] (* A329987 *)
%t Table[Floor[n*2^r], {n, 1, 250}] (* A329988 *)
%Y Cf. A329825, A329986, A329988 (complement).
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jan 02 2020