A140979 a(n) = floor(2*phi*floor(n*phi)) where phi = A001622.

3, 9, 12, 19, 25, 29, 35, 38, 45, 51, 55, 61, 67, 71, 77, 80, 87, 93, 97, 103, 106, 113, 119, 122, 129, 135, 139, 145, 148, 155, 161, 165, 171, 177, 181, 187, 190, 197, 203, 207, 213, 216, 223, 229, 232, 239, 245, 249, 255, 258, 265, 271, 275, 281, 284, 291, 297, 300, 307, 313, 317, 323, 326, 333, 339, 343, 349, 355

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Shiri Artstein-Avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, Discr. Math. 308 (2008), 4578-4588.

Shiri Artstein-Avidan, Aviezri S. Fraenkel and Vera T. Sos, A two-parameter family of an extension of Beatty sequences, preprint.

Maple

Digits := 200: a001622:= (1+sqrt(5))/2 : A140979 := proc(n) global a001622 ; floor(2*a001622*floor(n*a001622)) ; end: for n from 1 to 100 do printf("%d, ", A140979(n)); end: # R. J. Mathar, Sep 05 2008

Mathematica

Table[Floor[2*GoldenRatio*Floor[n*GoldenRatio]], {n, 70}] (* Harvey P. Dale, Feb 25 2018 *)

Prog

(Python)
from math import isqrt
def A140979(n): return (m:=n+isqrt(5*n**2)&-2)+isqrt(5*m**2)>>1 # Chai Wah Wu, Aug 29 2022

Crossrefs

Cf. A000201, A001622.

Sequence in context: A356220 A309394 A285564 * A096726 A272027 A310323

Adjacent sequences: A140976 A140977 A140978 * A140980 A140981 A140982

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 04 2008

Extensions

Definition corrected and more terms from R. J. Mathar, Sep 05 2008

Status

approved