This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A100585 #45 Sep 12 2024 21:40:13
%S A100585 3,4,5,6,8,10,13,17,22,29,38,50,66,88,117,156,208,277,369,492,656,874,
%T A100585 1165,1553,2070,2760,3680,4906,6541,8721,11628,15504,20672,27562,
%U A100585 36749,48998,65330,87106,116141,154854,206472,275296,367061,489414,652552
%N A100585 a(n+1) = a(n)+floor(a(n)/3), a(1) = 3.
%C A100585 Original definition: Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off every 4th term. Repeat, always crossing off every 4th term of those that remain. The numbers that are left form the sequence.
%C A100585 Can be stated as the number of animals starting from a single trio if any trio of animals can produce a single offspring. See A061418 for the equivalent sequence for pairs of animals. - _Luca Khan_, Sep 05 2024
%H A100585 Robert Israel, <a href="/A100585/b100585.txt">Table of n, a(n) for n = 1..7987</a>
%H A100585 Popular Computing (Calabasas, CA), <a href="/A003309/a003309.pdf">Sieves: Problem 43</a>, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #6 with K=4. [Annotated and scanned copy]
%H A100585 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A100585 a(1)=3, a(n+1) = a(n) + floor(a(n)/3). - _Ben Paul Thurston_, Jan 09 2008
%p A100585 R:= 3: x:= 3:
%p A100585 for i from 2 to 100 do x:= x + floor(x/3); R:= R,x od:
%p A100585 R; # _Robert Israel_, Sep 09 2024
%t A100585 t = Range[3, 2500000]; r = {}; While[Length[t] > 0, AppendTo[r, First[t]]; t = Drop[t, {1, -1, 4}];]; r (* _Ray Chandler_, Dec 02 2004 *)
%t A100585 NestList[#+Floor[#/3]&,3,50] (* _Harvey P. Dale_, Jan 14 2019 *)
%o A100585 (PARI) a(n,s=3)=for(i=2,n,s+=s\3);s \\ _M. F. Hasler_, Oct 06 2014
%Y A100585 Cf. A003309, A003310, A100464, A100562, A003312, A003311, A052548, A100586, A061418.
%K A100585 nonn
%O A100585 1,1
%A A100585 _N. J. A. Sloane_, Dec 01 2004
%E A100585 More terms from _Ray Chandler_, Dec 02 2004
%E A100585 Simpler definition from _M. F. Hasler_, Oct 06 2014