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A277645 Beatty sequence for 3+sqrt(6).

%I A277645 #25 Feb 16 2025 08:33:37
%S A277645 5,10,16,21,27,32,38,43,49,54,59,65,70,76,81,87,92,98,103,108,114,119,
%T A277645 125,130,136,141,147,152,158,163,168,174,179,185,190,196,201,207,212,
%U A277645 217,223,228,234,239,245,250,256,261,267,272,277,283,288,294,299,305
%N A277645 Beatty sequence for 3+sqrt(6).
%C A277645 Eggleton et al. show that k is in this sequence if and only if A277515(k) > 3.
%D A277645 R. B. Eggleton, J. S. Kimberley, and J. A. MacDougall, Square-free rank of integers, submitted.
%H A277645 Jason Kimberley, <a href="/A277645/b277645.txt">Table of n, a(n) for n = 1..10000</a>
%H A277645 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.
%H A277645 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>.
%F A277645 a(n) = floor(n*(3+sqrt(6))).
%F A277645 a(n) = 3*n + A000196(A033581(n)).
%F A277645 a(n) = A008585(n) + A000196(A033581(n)).
%e A277645 a(4) = 3*4 + 9 because 9^2 = 81 < 6*4^2 = 96 < 100 = 10^2.
%t A277645 Floor[Range[100]*(3 + Sqrt[6])] (* _Paolo Xausa_, Jul 11 2024 *)
%o A277645 (Magma) [3*n+Isqrt(6*n^2): n in [1..60]];
%Y A277645 Cf. A000196, A008585, A010464, A033581, A277515.
%Y A277645 Complement of A277644.
%K A277645 nonn,easy
%O A277645 1,1
%A A277645 _Jason Kimberley_, Oct 26 2016