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%I #4 Jan 02 2020 08:23:13
%S 2,4,7,9,11,14,16,18,21,23,25,28,30,32,35,37,39,42,44,46,49,51,53,56,
%T 58,60,63,65,67,70,72,75,77,79,82,84,86,89,91,93,96,98,100,103,105,
%U 107,110,112,114,117,119,121,124,126,128,131,133,135,138,140,142
%N Beatty sequence for (13+sqrt(109))/10.
%C Let r = (13+sqrt(109))/10. Then (floor(n*r)) and (floor(n*r + 3r/5)) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.
%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*s), where s = (13+sqrt(109))/10.
%t t = 3/5; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
%t Table[Floor[r*n], {n, 1, 200}] (* A329841 *)
%t Table[Floor[s*n], {n, 1, 200}] (* A329842 *)
%Y Cf. A329825, A329841 (complement).
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 31 2019
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