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%I #29 Nov 01 2019 16:46:14
%S 3,4,5,6,8,10,13,17,22,29,38,50,66,88,117,156,208,277,369,492,656,874,
%T 1165,1553,2070,2760,3680,4906,6541,8721,11628,15504,20672,27562,
%U 36749,48998,65330,87106,116141,154854,206472,275296,367061,489414,652552
%N a(n+1) = a(n)+floor(a(n)/3), a(1) = 3.
%C 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.
%H 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 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F a(1)=3, a(n+1) = a(n) + floor(a(n)/3). - _Ben Paul Thurston_, Jan 09 2008
%t 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 NestList[#+Floor[#/3]&,3,50] (* _Harvey P. Dale_, Jan 14 2019 *)
%o (PARI) a(n,s=3)=for(i=2,n,s+=s\3);s \\ _M. F. Hasler_, Oct 06 2014
%Y Cf. A003309, A003310, A100464, A100562, A003312, A003311, A052548, A100586.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Dec 01 2004
%E More terms from _Ray Chandler_, Dec 02 2004
%E Simpler definition from _M. F. Hasler_, Oct 06 2014
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