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

%I A022838 #71 Feb 16 2025 08:32:34
%S A022838 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 A022838 43,45,46,48,50,51,53,55,57,58,60,62,64,65,67,69,71,72,74,76,77,79,81,
%U A022838 83,84,86,88,90,91,93,95,96,98,100,102,103,105,107,109,110,112
%N A022838 Beatty sequence for sqrt(3); complement of A054406.
%C A022838 0 <= A144077(n) - a(n) <= 1. - _Reinhard Zumkeller_, Sep 09 2008
%C A022838 From _Reinhard Zumkeller_, Jan 20 2010: (Start)
%C A022838 A080757(n) = a(n+1) - a(n).
%C A022838 A171970(n) = floor(a(n)/2).
%C A022838 A171972(n) = a(A000290(n)). (End)
%C A022838 Numbers k>0 such that A194979(k+1) = A194979(k) + 1. - _Clark Kimberling_, Dec 02 2014
%C A022838 Powers of 2 (i.e, 1, 8, 32, 64, 128, 256, 512, 4096, 8192,...) appear at n=1, 5, 19, 37, 74, 148, 296, 2365, 4730, 18919, 75675, 151349, 302698, 605396, ... related to A293328. - _R. J. Mathar_, Jan 17 2025
%H A022838 Reinhard Zumkeller, <a href="/A022838/b022838.txt">Table of n, a(n) for n = 1..10000</a>
%H A022838 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 A022838 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A022838 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A022838 a(n) = floor(n*sqrt(3)). - _Reinhard Zumkeller_, Jan 20 2010
%F A022838 a(n) = 2 * floor(n * (sqrt(3) - 1)) + floor(n * (2 - sqrt(3))) + 1. - _Miko Labalan_, Dec 03 2016
%p A022838 A022838 := proc(n)
%p A022838     floor(n*sqrt(3)) ;
%p A022838 end proc: # _R. J. Mathar_, Mar 25 2013
%t A022838 Table[Floor[n 3^(1/2)] , {n, 1, 65}] (* _Geoffrey Critzer_, Jan 11 2015 *)
%o A022838 (Haskell)
%o A022838 a022838 = floor . (* sqrt 3) . fromIntegral
%o A022838 -- _Reinhard Zumkeller_, Sep 14 2014
%o A022838 (PARI) vector(60, n, floor(n*sqrt(3))) \\ _G. C. Greubel_, Sep 28 2018
%o A022838 (PARI) a(n)=sqrtint(3*n^2) \\ _Charles R Greathouse IV_, Nov 01 2021
%o A022838 (Magma) [Floor(n*Sqrt(3)): n in [1..60]]; // _G. C. Greubel_, Sep 28 2018
%o A022838 (Python)
%o A022838 from math import isqrt
%o A022838 def A022838(n): return isqrt(3*n*n) # _Chai Wah Wu_, Aug 06 2022
%Y A022838 Cf. A080757 (first differences), A194106 (partial sums), A194028 (even bisection), A184796 (prime terms).
%Y A022838 Cf. A026255, A054406 (complement).
%K A022838 nonn
%O A022838 1,2
%A A022838 _Clark Kimberling_