%I #9 Jul 09 2024 08:41:44

%S 1,3,4,6,7,9,10,12,13,15,16,18,20,21,23,24,26,27,29,30,32,33,35,37,38,

%T 40,41,43,44,46,47,49,50,52,54,55,57,58,60,61,63,64,66,67,69,71,72,74,

%U 75,77,78,80,81,83,84,86,87,89,91,92,94,95,97,98,100,101,103,104,106

%N A Beatty sequence: a(n) = [n*(1+1/t)], where t = tribonacci constant (A058265); complement of A140099.

%H N. J. A. Sloane, <a href="/A140098/b140098.txt">Table of n, a(n) for n = 1..20000</a>

%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>.

%e Tribonacci constant: t = 1.839286755214161132551852564653286600...

%e 1 + 1/t = 1.54368901269207636157085597180174798652520...

%t Floor[Range[100]*(1 + 1/Root[#^3-#^2-#-1 &, 1])] (* _Paolo Xausa_, Jul 09 2024 *)

%o (PARI) {a(n)=local(t=(1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3))/3);floor(n*(1+1/t))}

%Y Cf. A140099, A140100, A058265.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 01 2008