|
| |
|
|
A005653
|
|
Sum of 2 terms is never a Fibonacci number.
(Formerly M0965)
|
|
16
| |
|
|
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; 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 (ck6(AT)evansville.edu), 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 A092311 A186386
Adjacent sequences: A005650 A005651 A005652 * A005654 A005655 A005656
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com), N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2002
|
| |
|
|
