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A022838 Beatty sequence for sqrt(3); complement of A054406. 63
1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 45, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 90, 91, 93, 95, 96, 98, 100, 102, 103, 105, 107, 109, 110, 112 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
0 <= A144077(n) - a(n) <= 1. - Reinhard Zumkeller, Sep 09 2008
From Reinhard Zumkeller, Jan 20 2010: (Start)
A080757(n) = a(n+1) - a(n).
A171970(n) = floor(a(n)/2).
A171972(n) = a(A000290(n)). (End)
Numbers k>0 such that A194979(k+1) = A194979(k) + 1. - Clark Kimberling, Dec 02 2014
LINKS
Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.
Eric Weisstein's World of Mathematics, Beatty Sequence.
FORMULA
a(n) = floor(n*sqrt(3)). - Reinhard Zumkeller, Jan 20 2010
a(n) = 2 * floor(n * (sqrt(3) - 1)) + floor(n * (2 - sqrt(3))) + 1. - Miko Labalan, Dec 03 2016
MAPLE
A022838 := proc(n)
floor(n*sqrt(3)) ;
end proc: # R. J. Mathar, Mar 25 2013
MATHEMATICA
Table[Floor[n 3^(1/2)] , {n, 1, 65}] (* Geoffrey Critzer, Jan 11 2015 *)
PROG
(Haskell)
a022838 = floor . (* sqrt 3) . fromIntegral
-- Reinhard Zumkeller, Sep 14 2014
(PARI) vector(60, n, floor(n*sqrt(3))) \\ G. C. Greubel, Sep 28 2018
(PARI) a(n)=sqrtint(3*n^2) \\ Charles R Greathouse IV, Nov 01 2021
(Magma) [Floor(n*Sqrt(3)): n in [1..60]]; // G. C. Greubel, Sep 28 2018
(Python)
from math import isqrt
def A022838(n): return isqrt(3*n*n) # Chai Wah Wu, Aug 06 2022
CROSSREFS
Cf. A080757 (first differences), A194106 (partial sums), A194028 (even bisection), A184796 (prime terms).
Cf. A026255, A054406 (complement).
Sequence in context: A329829 A182760 A292646 * A329841 A047329 A187685
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)