OFFSET
1,2
COMMENTS
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
REFERENCES
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).
LINKS
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.
FORMULA
a(n) = floor[n*(1+tau)-tau/2] =floor[n*2.6180...-0.8090...]. - Henry Bottomley, Sep 03 2001
MATHEMATICA
max = 100; Complement[ Range[ max*GoldenRatio], Round[ Range[max]*GoldenRatio]] (* Jean-François Alcover, Oct 10 2011 *)
PROG
(PARI) a(n) = tau=(1+sqrt(5))/2; floor(n*(1+tau) - tau/2) \\ Michel Marcus, May 21 2013
(Python)
from math import isqrt
def A007064(n): return (6*n-1+isqrt(5*((n<<1)-1)**2))>>2 # Chai Wah Wu, Feb 11 2025
CROSSREFS
KEYWORD
nonn,easy,nice,changed
AUTHOR
STATUS
approved