A057843 a(n) = floor(n*tau^2) - 3, where tau = (1+sqrt(5))/2.

-1, 2, 4, 7, 10, 12, 15, 17, 20, 23, 25, 28, 31, 33, 36, 38, 41, 44, 46, 49, 51, 54, 57, 59, 62, 65, 67, 70, 72, 75, 78, 80, 83, 86, 88, 91, 93, 96, 99, 101, 104, 106, 109, 112, 114, 117, 120, 122, 125, 127, 130, 133, 135, 138, 140, 143, 146, 148, 151, 154, 156, 159

Offset

1,2

Comments

This sequence and A007064 are very similar - this can be seen if the terms equal to 4 are aligned. - Thomas Baruchel, Nov 04 2003

Links

Table of n, a(n) for n=1..62.

Jon Asier Bárcena-Petisco, Luis Martínez, María Merino, Juan Manuel Montoya, and Antonio Vera-López, Fibonacci-like partitions and their associated piecewise-defined permutations, arXiv:2503.19696 [math.CO], 2025. See p. 3.

Johan Kok, Integer sequences with conjectured relation with certain graph parameters of the family of linear Jaco graphs, arXiv:2507.16500 [math.CO], 2025. See pp. 5-6.

Mathematica

Floor[GoldenRatio^2 Range[70]]-3 (* Harvey P. Dale, May 15 2014 *)

Prog

(PARI) a(n)=(3+sqrt(5))*n\2 - 3 \\ Charles R Greathouse IV, Jan 23 2015
(Python)
from math import isqrt
def A057843(n): return 3*(n-2)+isqrt(5*n**2)>>1 # Chai Wah Wu, Jun 11 2026

Crossrefs

Subtract 2 from each term of A003622. Complement of A058065.

Sequence in context: A164903 A285968 A218772 * A047539 A190521 A186224

Adjacent sequences: A057840 A057841 A057842 * A057844 A057845 A057846

Keyword

sign

Author

N. J. A. Sloane, Nov 24 2000

Status

approved