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Search: id:A005653
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| A005653 |
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Sum of 2 terms is never a Fibonacci number.
(Formerly M0965)
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+0
5
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 less than n (Chow-Long).
Numbers n such that 2{n*phi}={2n*phi}, 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[130], f[ # ] == 0 &]
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CROSSREFS
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Complement of A005652. See A078588 for further comments.
Sequence in context: A153766 A093013 A047495 this_sequence A092311 A058212 A007997
Adjacent sequences: A005650 A005651 A005652 this_sequence A005654 A005655 A005656
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com), N. J. A. Sloane (njas(AT)research.att.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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