A329830 - OEIS

%I #4 Jan 02 2020 08:19:58

%S 2,4,7,9,11,14,16,19,21,23,26,28,31,33,35,38,40,42,45,47,50,52,54,57,

%T 59,62,64,66,69,71,74,76,78,81,83,85,88,90,93,95,97,100,102,105,107,

%U 109,112,114,116,119,121,124,126,128,131,133,136,138,140,143,145

%N Beatty sequence for (4+sqrt(10))/3.

%C Let r = (2+sqrt(10))/3. Then (floor(n*r)) and (floor(n*r + 2r/3)) 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*s), where s = (4+sqrt(10))/3.

%t t = 2/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];

%t Table[Floor[r*n], {n, 1, 200}]   (* A329829 *)

%t Table[Floor[s*n], {n, 1, 200}]   (* A329830 *)

%Y Cf. A329825, A329829 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Dec 31 2019