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A001690 Non-Fibonacci numbers.
(Formerly M3268 N1319)
24
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; text; internal format)
OFFSET

1,1

COMMENTS

A010056(a(n)) = 0. - Reinhard Zumkeller, Oct 10 2013

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Bakir Farhi, An explicit formula generating the non-Fibonacci numbers, arXiv:1105.1127 [math.NT], May 05 2011.

H. W. Gould, Non-Fibonacci numbers, Fib. Quart., 3 (1965), pp. 177-183.

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

a(n) ~ n. - Charles R Greathouse IV, Nov 06 2014

MATHEMATICA

Complement[Range[Fibonacci[a = 20]], Fibonacci[Range[a]]] (* Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)

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)) /* Joerg Arndt, May 14 2011 */

(PARI) lower=3; upper=5; for(i=4, 20, for(n=lower+1, upper-1, print1(n", ")); [lower, upper]=[upper, lower+upper]) \\ Charles R Greathouse IV, Nov 19 2013

(Haskell)

a001690 n = a001690_list !! (n-1)

a001690_list = filter ((== 0) . a010056) [0..]

-- Reinhard Zumkeller, Oct 10 2013

(Python)

def f(n):

    a=1

    b=2

    c=3

    while n>0:

        a=b

        b=c

        c=a+b

        n-=(c-b-1)

    n+=(c-b-1)

    return (b+n)

for i in range(1, 1001):

    print str(i)+" "+str(f(i)) \\ Indranil Ghosh, Dec 22 2016

CROSSREFS

The nonnegative integers that are not in A000045.

Cf. A010056.

Sequence in context: A269330 A213627 A225871 * A105447 A242286 A144222

Adjacent sequences:  A001687 A001688 A001689 * A001691 A001692 A001693

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 20 15:11 EST 2017. Contains 282390 sequences.