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A001690
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Non-Fibonacci numbers.
(Formerly M3268 N1319)
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14
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4, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| H. W. Gould, Non-Fibonacci numbers, Fib. Quart., 3 (1965), 177-183.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Bakir Farhi, An explicit formula generating the non-Fibonacci numbers, May 05 2011.
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FORMULA
| a(n-1)=floor(n+lgg(sqrt(5)*(lgg(sqrt(5)*n)+n)-5+3/n)-2) where lgg(x)=log(x)/log((sqrt(5)+1)/2), given by Farhi. [Jonathan Vos Post, May 05 2011]
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MATHEMATICA
| Complement[Range[Fibonacci[a = 20]], Fibonacci[Range[a]]] (* From Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)
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PROG
| (PARI) lgg(x)=log(x)/log((sqrt(5)+1)/2);
a(n)=n++; floor(n+lgg(sqrt(5)*(lgg(sqrt(5)*n)+n)-5+3/n)-2);
vector(66, n, a(n)) /* show terms */ /* Joerg Arndt, May 14 2011 */
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CROSSREFS
| The nonnegative integers that are not in A000045.
Sequence in context: A024554 A078744 A024555 * A105447 A144222 A010414
Adjacent sequences: A001687 A001688 A001689 * A001691 A001692 A001693
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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