The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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*ceiling(n*phi) - ceiling(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. Positions of 1's in {A078588(n) : n > 0}. - Clark Kimberling and Jianing Song, Sep 10 2019 Also positive integers k such that {k*r} > 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part. - Clark Kimberling and Jianing Song, Sep 12 2019 REFERENCES 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 K. Alladi et al., On additive partitions of integers, Discrete Math., 22 (1978), 201-211. 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 Positive integers such that A078588(n) = 1. - Clark Kimberling and Jianing Song, Sep 10 2019 MATHEMATICA f[n_] := Block[{k = Floor[n/GoldenRatio]}, If[n - k*GoldenRatio > (k + 1)*GoldenRatio - n, 1, 0]]; Select[ Range, f[ # ] == 1 &] r = (1 + Sqrt)/2; z = 300; t = Table[Floor[2 n*r] - 2 Floor[n*r], {n, 1, z}] (* {A078588(n) : n > 0} *) Flatten[Position[t, 0]] (* A005653 *) Flatten[Position[t, 1]] (* A005652 *) (* Clark Kimberling and Jianing Song, Sep 10 2019 *) r = GoldenRatio; t = Table[If[FractionalPart[n*r] < 1/2, 0, 1 ], {n, 1, 120}] (* {A078588(n) : n > 0} *) Flatten[Position[t, 0]]  (* A005653 *) Flatten[Position[t, 1]]  (* A005652 *) (* Clark Kimberling and Jianing Song, Sep 12 2019 *) CROSSREFS Complement of A005653. Equals A279934 - 1. 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 EXTENSIONS Extended by Robert G. Wilson v, Dec 02 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 11 12:38 EDT 2021. Contains 342886 sequences. (Running on oeis4.)