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A005652 Sum of 2 terms is never a Fibonacci number.
(Formerly M2517)
24
1, 3, 6, 8, 9, 11, 14, 16, 17, 19, 21, 22, 24, 27, 29, 30, 32, 35, 37, 40, 42, 43, 45, 48, 50, 51, 53, 55, 56, 58, 61, 63, 64, 66, 69, 71, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 95, 97, 98, 100, 103, 105, 106, 108, 110, 111, 113, 116, 118, 119, 121, 124, 126, 129, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, n such that n = 2*ceil(n*phi)-ceil(n*sqrt(5)) where phi = (1+sqrt(5))/2. - Benoit Cloitre, Dec 05 2002

The Chow-Long paper gives a connection with continued fractions, as well as generalizations and other references for this and related sequences.

REFERENCES

K. Alladi et al., On additive partitions of integers, Discrete Math., 22 (1978), 201-211.

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

T. Y. Chow and C. D. Long, Additive partitions and continued fractions, Ramanujan J., 3 (1999), 55-72 [set alpha=(1+sqrt(5))/2 in Theorem 2 to get A005652 and A005653].

FORMULA

The set of all n such that the integer multiple of (1+sqrt(5))/2 nearest n is greater than n (Chow-Long).

Numbers n such that 2{n*phi}-{2n*phi}=1, where { } denotes fractional part. - Clark Kimberling, Jan 01 2007

MATHEMATICA

f[n_] := Block[{k = Floor[n/GoldenRatio]}, If[n - k*GoldenRatio > (k + 1)*GoldenRatio - n, 1, 0]]; Select[ Range[131], f[ # ] == 1 &]

CROSSREFS

Complement of A005653. See A078588 for further comments.

Sequence in context: A231010 A285250 A188469 * A047401 A187952 A188028

Adjacent sequences:  A005649 A005650 A005651 * A005653 A005654 A005655

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

Extended by Robert G. Wilson v, Dec 02 2002

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)