A022839 Beatty sequence for sqrt(5).
2, 4, 6, 8, 11, 13, 15, 17, 20, 22, 24, 26, 29, 31, 33, 35, 38, 40, 42, 44, 46, 49, 51, 53, 55, 58, 60, 62, 64, 67, 69, 71, 73, 76, 78, 80, 82, 84, 87, 89, 91, 93, 96, 98, 100, 102, 105, 107, 109, 111, 114, 116, 118, 120, 122, 125, 127, 129, 131, 134, 136
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- R. L. Graham, S. Lin and C.-S. Lin, Spectra of numbers, Math. Mag. 51 (1978), 174-176.
- Index entries for sequences related to Beatty sequences
Programs
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Magma
[Floor(n*Sqrt(5)): n in [1..60]]; // Vincenzo Librandi, Oct 22 2011
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Maple
a:=n->floor(n*sqrt(5)): seq(a(n),n=1..70); # Muniru A Asiru, Sep 28 2018
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Mathematica
With[{c=Sqrt[5]},Floor[c*Range[70]]] (* Harvey P. Dale, Mar 19 2012 *) -
PARI
vector(60, n, floor(n*sqrt(5))) \\ G. C. Greubel, Sep 28 2018
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PARI
a(n)=sqrtint(5*n^2) \\ Charles R Greathouse IV, Jan 24 2022
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Python
from math import isqrt def A022839(n): return isqrt(5*n**2) # Chai Wah Wu, Sep 07 2022
Formula
a(n) = floor(n*sqrt(5)). - G. C. Greubel, Sep 28 2018