A329848 - OEIS

%I #4 Jan 02 2020 16:15:01

%S 2,5,8,11,14,16,19,22,25,28,30,33,36,39,42,44,47,50,53,56,58,61,64,67,

%T 70,72,75,78,81,84,86,89,92,95,98,100,103,106,109,112,114,117,120,123,

%U 126,128,131,134,137,140,143,145,148,151,154,157,159,162,165

%N Beatty sequence for (13+sqrt(89))/8.

%C Let r = (3+sqrt(89))/8. Then (floor(n*r)) and (floor(n*r + 5r/4)) 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 = (13+sqrt(89))/8.

%t t = 5/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];

%t Table[Floor[r*n], {n, 1, 200}]   (* A329847 *)

%t Table[Floor[s*n], {n, 1, 200}]   (* A329848 *)

%Y Cf. A329825, A329847 (complement).

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jan 02 2020