A057843 -id:A057843 - cp's OEIS frontend

A058065 Complement of A057843.

0, 1, 3, 5, 6, 8, 9, 11, 13, 14, 16, 18, 19, 21, 22, 24, 26, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 64, 66, 68, 69, 71, 73, 74, 76, 77, 79, 81, 82, 84, 85, 87, 89, 90, 92, 94, 95, 97, 98, 100, 102, 103, 105, 107, 108, 110

Offset: 0

N. J. A. Sloane, Nov 24 2000

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.

Cf. A057843, A082389.

Table[Floor[n*GoldenRatio+Sqrt[5]],{n,0,100}]-2 (* Harvey P. Dale, Mar 01 2019 *)

a(n) = floor(tau*n+sqrt(5))-2 where tau is the Golden ratio = (1+sqrt(5))/2. - Benoit Cloitre, Apr 14 2003

A007064 Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.

Original entry on oeis.org

1, 4, 7, 9, 12, 14, 17, 20, 22, 25, 27, 30, 33, 35, 38, 41, 43, 46, 48, 51, 54, 56, 59, 62, 64, 67, 69, 72, 75, 77, 80, 82, 85, 88, 90, 93, 96, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 124, 127, 130, 132, 135

Offset: 1

N. J. A. Sloane, Mira Bernstein

First column of Stolarsky array.

This sequence and A057843 are very similar - this can be seen if the terms equal to 4 are aligned. - Thomas Baruchel, Nov 04 2003

Clark Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Benoit Cloitre and Jeffrey Shallit, Some Fibonacci-Related Sequences, arXiv:2312.11706 [math.CO], 2023.
Clark Kimberling, Interspersions
Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society 117 (1993) 313-321.
N. J. A. Sloane, Classic Sequences
K. B. Stolarsky, A set of generalized Fibonacci sequences such that each natural number belongs to exactly one, Fib. Quart., 15 (1977), 224.

Complement of A007067.

Cf. A001622, A035506.

max = 100; Complement[ Range[ max*GoldenRatio], Round[ Range[max]*GoldenRatio]] (* Jean-François Alcover, Oct 10 2011 *)

a(n) = tau=(1+sqrt(5))/2; floor(n*(1+tau) - tau/2) \\ Michel Marcus, May 21 2013

from math import isqrt
def A007064(n): return (6*n-1+isqrt(5*((n<<1)-1)**2))>>2 # Chai Wah Wu, Feb 11 2025

a(n) = floor[n*(1+tau)-tau/2] =floor[n*2.6180...-0.8090...]. - Henry Bottomley, Sep 03 2001

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A058065 Complement of A057843.

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A007064 Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.

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