A184808 n + floor(r*n), where r = sqrt(2/3); complement of A184809.

1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 19, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 39, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 59, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 79, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 99, 101, 103, 105, 107, 108, 110, 112, 114, 116

Offset

1,2

Comments

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

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

Also, numbers n such that floor((n+1)*sqrt(6)) - floor(n*sqrt(6)) = 2. - Clark Kimberling, Jul 15 2015

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Formula

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

Mathematica

r=(2/3)^(1/2); s=(3/2)^(1/2);
a[n_]:=n+Floor [n*r];
b[n_]:=n+Floor [n*s];
Table[a[n], {n, 1, 120}]  (* A184808 *)
Table[b[n], {n, 1, 120}]  (* A184809 *)

Prog

(Magma) [n+Floor(n*Sqrt(2/3)): n in [1..70]]; // Vincenzo Librandi, Oct 23 2014
(PARI)
main(size)={return(vector(size, n, n+floor(sqrt(2/3)*n)))} /* Anders Hellström, Jul 15 2015 */

Crossrefs

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

A184810, A184811, A249096.

Sequence in context: A187318 A262770 A108598 * A329837 A214315 A249098

Adjacent sequences: A184805 A184806 A184807 * A184809 A184810 A184811

Keyword

nonn

Author

Clark Kimberling, Jan 22 2011

Status

approved