

A007064


Numbers not of form "nearest integer to n*tau", tau=(1+sqrt(5))/2.
(Formerly M3298)


11



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
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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 (baruchel(AT)users.sourceforge.net), Nov 04 2003


REFERENCES

C. Kimberling, "Interspersions and dispersions," Proceedings of the American Mathematical Society 117 (1993) 313321.
C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129138.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
K. B. Stolarsky, A set of generalized Fibonacci sequences such that each natural number belongs to exactly one, Fib. Quart., 15 (1977), 224.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. Kimberling, Interspersions
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]] (* JeanFrançois 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. Cf. A035506.
Sequence in context: A092861 A007072 A186323 * A086824 A080574 A189367
Adjacent sequences: A007061 A007062 A007063 * A007065 A007066 A007067


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane, Mira Bernstein


STATUS

approved



