A184808 - OEIS

%I #22 Sep 08 2022 08:45:55

%S 1,3,5,7,9,10,12,14,16,18,19,21,23,25,27,29,30,32,34,36,38,39,41,43,

%T 45,47,49,50,52,54,56,58,59,61,63,65,67,69,70,72,74,76,78,79,81,83,85,

%U 87,89,90,92,94,96,98,99,101,103,105,107,108,110,112,114,116

%N n + floor(r*n), where r = sqrt(2/3); complement of A184809.

%C This is the Beatty sequence for 1 + sqrt(2/3).

%C Also, a(n) is the position of 2*n^2 in the sequence obtained by arranging all the numbers in the sets {2*h^2, h >= 1} and {3*k^2, k >= 1} in increasing order. - _Clark Kimberling_, Oct 20 2014

%C Also, numbers n such that floor((n+1)*sqrt(6)) - floor(n*sqrt(6)) = 2. - _Clark Kimberling_, Jul 15 2015

%H Clark Kimberling, <a href="/A184808/b184808.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n + floor(r*n), where r = sqrt(2/3).

%t r=(2/3)^(1/2); s=(3/2)^(1/2);

%t a[n_]:=n+Floor [n*r];

%t b[n_]:=n+Floor [n*s];

%t Table[a[n],{n,1,120}]  (* A184808 *)

%t Table[b[n],{n,1,120}]  (* A184809 *)

%o (Magma) [n+Floor(n*Sqrt(2/3)): n in [1..70]]; // _Vincenzo Librandi_, Oct 23 2014

%o (PARI)

%o main(size)={return(vector(size, n, n+floor(sqrt(2/3)*n)))} /* _Anders Hellström_, Jul 15 2015 */

%Y Cf. A184809, A182760 (comment about joint ranking),

%Y A184810, A184811, A249096.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 22 2011