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A066096 a(n) = floor(n*phi), where phi = (1 + sqrt(5))/2. 26
0, 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105, 106 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(n) is the smallest number different from a(i) and a(i)+i for i < n.
The losing positions in the game of Wythoff-Nim are precisely the pairs (a(n), a(n)+n).
LINKS
FORMULA
Duplicate values in A060143.
a(n) = 1 + A022342(n) = A000201(n).
a(n) = floor(n*phi), where phi = (1 + sqrt(5))/2. - Peter Munn, Jan 12 2018
a(n) = A026351(n) - 1. - Philippe Deléham, Jan 15 2023
MATHEMATICA
Floor[GoldenRatio*Range[0, 80]] (* G. C. Greubel, Sep 12 2023 *)
PROG
(PARI) a(n) = (n+sqrtint(5*n^2))\2;
[a(n)|n<-[0..100]] \\ Simon Strandgaard, Jun 28 2022
(Magma) [Floor((1+Sqrt(5))*n/2): n in [0..80]]; // G. C. Greubel, Sep 12 2023
(SageMath) [floor(golden_ratio*n) for n in range(81)] # G. C. Greubel, Sep 12 2023
CROSSREFS
Essentially the partial sums of A001468.
Sequence in context: A285676 A085270 A330063 * A000201 A090908 A292644
KEYWORD
nonn,easy
AUTHOR
Michele Dondi (bik.mido(AT)tiscalenet.it), Dec 30 2001
EXTENSIONS
Name corrected by Peter Munn, Dec 06 2017
New name using a formula from Peter Munn by Peter Luschny, Jan 18 2023
STATUS
approved

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Last modified April 22 15:04 EDT 2024. Contains 371905 sequences. (Running on oeis4.)