

A007064


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


12



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, Nov 04 2003


REFERENCES

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).


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. Kimberling, Interspersions
C. Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society 117 (1993) 313321.
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]] (* 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: A248561 A007072 A186323 * A007073 A279054 A086824
Adjacent sequences: A007061 A007062 A007063 * A007065 A007066 A007067


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane, Mira Bernstein


STATUS

approved



