A022838 Beatty sequence for sqrt(3); complement of A054406.

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

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Clark Kimberling, Beatty sequences and trigonometric functions, Integers 16 (2016), #A15.

Eric Weisstein's World of Mathematics, Beatty Sequence.

Index entries for sequences related to Beatty sequences

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

Adjacent sequences: A022835 A022836 A022837 * A022839 A022840 A022841

Keyword

nonn

Author

Clark Kimberling

Status

approved