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A022838 Beatty sequence for sqrt(3); complement of A054406. 63

%I #66 Sep 08 2022 08:44:46

%S 1,3,5,6,8,10,12,13,15,17,19,20,22,24,25,27,29,31,32,34,36,38,39,41,

%T 43,45,46,48,50,51,53,55,57,58,60,62,64,65,67,69,71,72,74,76,77,79,81,

%U 83,84,86,88,90,91,93,95,96,98,100,102,103,105,107,109,110,112

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

%C 0 <= A144077(n) - a(n) <= 1. - _Reinhard Zumkeller_, Sep 09 2008

%C From _Reinhard Zumkeller_, Jan 20 2010: (Start)

%C A080757(n) = a(n+1) - a(n).

%C A171970(n) = floor(a(n)/2).

%C A171972(n) = a(A000290(n)). (End)

%C Numbers k>0 such that A194979(k+1) = A194979(k) + 1. - _Clark Kimberling_, Dec 02 2014

%H Reinhard Zumkeller, <a href="/A022838/b022838.txt">Table of n, a(n) for n = 1..10000</a>

%H Clark Kimberling, <a href="https://www.emis.de/journals/INTEGERS/papers/q15/q15.Abstract.html">Beatty sequences and trigonometric functions</a>, Integers 16 (2016), #A15.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(n) = floor(n*sqrt(3)). - _Reinhard Zumkeller_, Jan 20 2010

%F a(n) = 2 * floor(n * (sqrt(3) - 1)) + floor(n * (2 - sqrt(3))) + 1. - _Miko Labalan_, Dec 03 2016

%p A022838 := proc(n)

%p floor(n*sqrt(3)) ;

%p end proc: # _R. J. Mathar_, Mar 25 2013

%t Table[Floor[n 3^(1/2)] , {n, 1, 65}] (* _Geoffrey Critzer_, Jan 11 2015 *)

%o (Haskell)

%o a022838 = floor . (* sqrt 3) . fromIntegral

%o -- _Reinhard Zumkeller_, Sep 14 2014

%o (PARI) vector(60, n, floor(n*sqrt(3))) \\ _G. C. Greubel_, Sep 28 2018

%o (PARI) a(n)=sqrtint(3*n^2) \\ _Charles R Greathouse IV_, Nov 01 2021

%o (Magma) [Floor(n*Sqrt(3)): n in [1..60]]; // _G. C. Greubel_, Sep 28 2018

%o (Python)

%o from math import isqrt

%o def A022838(n): return isqrt(3*n*n) # _Chai Wah Wu_, Aug 06 2022

%Y Cf. A080757 (first differences), A194106 (partial sums), A194028 (even bisection), A184796 (prime terms).

%Y Cf. A026255, A054406 (complement).

%K nonn

%O 1,2

%A _Clark Kimberling_

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)