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Search: id:A005652
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| A005652 |
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Sum of 2 terms is never a Fibonacci number.
(Formerly M2517)
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+0
9
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Also, n such that n = 2*ceil(n*phi)-ceil(n*sqrt(5)) where phi = (1+sqrt(5))/2. - Benoit Cloitre (benoit7848c(AT)orange.fr), 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.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
K. Alladi et al., On additive partitions of integers, Discrete Math., 22 (1978), 201-211.
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LINKS
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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].
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FORMULA
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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 (ck6(AT)evansville.edu), Jan 01 2007
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MATHEMATICA
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f[n_] := Block[{k = Floor[n/GoldenRatio]}, If[n - k*GoldenRatio > (k + 1)*GoldenRatio - n, 1, 0]]; Select[ Range[131], f[ # ] == 1 &]
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CROSSREFS
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Complement of A005653. See A078588 for further comments.
Sequence in context: A004715 A036558 A005870 this_sequence A047401 A024707 A084020
Adjacent sequences: A005649 A005650 A005651 this_sequence A005653 A005654 A005655
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2002
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