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A007064 Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.
(Formerly M3298)
13
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 (list; graph; refs; listen; history; text; internal format)
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
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
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
CROSSREFS
Complement of A007067.
Sequence in context: A360925 A007072 A186323 * A007073 A279054 A086824
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)