A329845 - OEIS

%I #4 Jan 02 2020 16:14:42

%S 1,3,5,6,8,10,11,13,15,16,18,20,21,23,25,26,28,30,31,33,35,36,38,40,

%T 41,43,45,46,48,50,51,53,55,57,58,60,62,63,65,67,68,70,72,73,75,77,78,

%U 80,82,83,85,87,88,90,92,93,95,97,98,100,102,103,105,107

%N Beatty sequence for (3+sqrt(29))/5.

%C Let r = (3+sqrt(29))/5. Then (floor(n*r)) and (floor(n*r + 4r/5)) 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*r), where r = (3+sqrt(29))/5.

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

%t Table[Floor[r*n], {n, 1, 200}]   (* A329845 *)

%t Table[Floor[s*n], {n, 1, 200}]   (* A329846 *)

%Y Cf. A329825, A329846 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jan 02 2020