A014245 a(n) = (n-th term of Beatty sequence for (3+sqrt(3))/2) - (n-th term of Beatty sequence for sqrt(3)).

1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 42, 43, 44, 44, 45, 46, 46, 47

Offset

1,3

Comments

It appears that a(n) is the nearest integer to (3-sqrt(3))/2 * n. - Franklin T. Adams-Watters, Nov 02 2006

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor((3+sqrt(3))/2 * n) - floor(sqrt(3) * n).

Maple

a:=n->floor((3+sqrt(3))/2*n)-floor(sqrt(3)*n): seq(a(n), n=1..80); # Muniru A Asiru, Oct 17 2018

Mathematica

With[{r = Sqrt@ 3}, Array[Floor[# (3 + r)/2] - Floor[# r] &, 80] ] (* Michael De Vlieger, Oct 17 2018 *)

Prog

(PARI) my(r=sqrt(3)); vector(80, n, (n*r*(r+1))\2 - (n*r)\1) \\ G. C. Greubel, Jun 19 2019
(Magma) r:=Sqrt(3); [Floor(n*r*(r+1)/2) - Floor(n*r): n in [1..80]]; // G. C. Greubel, Jun 19 2019
(Sage) r=sqrt(3); [floor(n*r*(r+1)/2) - floor(n*r) for n in (1..80)] # G. C. Greubel, Jun 19 2019

Crossrefs

Cf. A054406, A022838.

Sequence in context: A005206 A309077 A057365 * A350969 A096386 A257063

Adjacent sequences: A014242 A014243 A014244 * A014246 A014247 A014248

Keyword

nonn

Author

Clark Kimberling

Extensions

Corrected and extended by Franklin T. Adams-Watters, Nov 02 2006

Extraneous comma following a(56) removed by Sean A. Irvine, Oct 17 2018

Status

approved