A329827 - OEIS

%I #10 Feb 16 2025 08:33:58

%S 1,3,5,7,9,11,12,14,16,18,20,22,24,25,27,29,31,33,35,36,38,40,42,44,

%T 46,48,49,51,53,55,57,59,60,62,64,66,68,70,72,73,75,77,79,81,83,84,86,

%U 88,90,92,94,96,97,99,101,103,105,107,108,110,112,114,116

%N Beatty sequence for (5+sqrt(37))/6.

%C Let r = (5+sqrt(37))/6. Then (floor(n*r)) and (floor(n*r + r/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="https://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 = (5+sqrt(37))/6.

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

%t Table[Floor[r*n], {n, 1, 200}]   (* A329827 *)

%t Table[Floor[s*n], {n, 1, 200}]   (* A329828 *)

%Y Cf. A329825, A329828 (complement).

%K nonn,easy,changed

%O 1,2

%A _Clark Kimberling_, Dec 31 2019