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A277644 Beatty sequence for sqrt(6)/2.

%I A277644 #25 Feb 16 2025 08:33:37
%S A277644 1,2,3,4,6,7,8,9,11,12,13,14,15,17,18,19,20,22,23,24,25,26,28,29,30,
%T A277644 31,33,34,35,36,37,39,40,41,42,44,45,46,47,48,50,51,52,53,55,56,57,58,
%U A277644 60,61,62,63,64,66,67,68,69,71,72,73,74,75,77,78,79,80,82,83,84,85,86
%N A277644 Beatty sequence for sqrt(6)/2.
%C A277644 Eggleton et al. show that k is in this sequence if and only if A277515(k)=3.
%D A277644 R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, submitted.
%H A277644 Jason Kimberley, <a href="/A277644/b277644.txt">Table of n, a(n) for n = 1..10000</a>
%H A277644 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.
%H A277644 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>.
%F A277644 a(n) = floor(n*sqrt(6)/2).
%F A277644 a(n) = A000196(A032528(n)).
%e A277644 a(5)=6 because the quotient of 3*5^2 by 2 is 37 which lies between 6^2 and 7^2.
%t A277644 Floor[Range[100]*Sqrt[3/2]] (* _Paolo Xausa_, Jul 11 2024 *)
%o A277644 (Magma) [Isqrt(3*n^2 div 2): n in [1..60]];
%o A277644 (PARI) a(n)=sqrtint(3*n^2\2) \\ _Charles R Greathouse IV_, Jul 11 2024
%Y A277644 Cf. A000196, A032528, A115754, A277515. Complement of A277645.
%K A277644 nonn,easy
%O A277644 1,2
%A A277644 _Jason Kimberley_, Oct 26 2016