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A005653 Sum of 2 terms is never a Fibonacci number.
(Formerly M0965)
17
2, 4, 5, 7, 10, 12, 13, 15, 18, 20, 23, 25, 26, 28, 31, 33, 34, 36, 38, 39, 41, 44, 46, 47, 49, 52, 54, 57, 59, 60, 62, 65, 67, 68, 70, 72, 73, 75, 78, 80, 81, 83, 86, 88, 89, 91, 93, 94, 96, 99, 101, 102, 104, 107, 109, 112, 114, 115, 117, 120, 122, 123, 125, 127, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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 less than n (Chow-Long).

Numbers n such that 2{n*phi}={2n*phi}, 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[130], f[ # ] == 0 &]

CROSSREFS

Complement of A005652. See A078588 for further comments.

Sequence in context: A188029 A187951 A047495 * A188468 A285251 A231013

Adjacent sequences:  A005650 A005651 A005652 * A005654 A005655 A005656

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe, N. J. A. Sloane.

EXTENSIONS

Extended by Robert G. Wilson v, Dec 02 2002

STATUS

approved

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Last modified February 22 07:53 EST 2018. Contains 299447 sequences. (Running on oeis4.)