%I A003312 M2308
%S A003312 3,4,5,7,10,14,20,29,43,64,95,142,212,317,475,712,1067,1600,2399,3598,
               5396,
%T A003312 8093,12139,18208,27311,40966,61448,92171,138256,207383,311074,466610,
               699914,
%U A003312 1049870,1574804,2362205,3543307,5314960,7972439,11958658,17937986,26906978
%N A003312 a(1) = 3; for n>0, a(n+1) = a(n) + [ (a(n)-1)/2 ].
%C A003312 This sequence originally defined in the 1974 reference by a sieve, as 
               follows. 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 
               third term. Repeat, always crossing off every third term of those 
               that remain. The numbers that are left form the sequence. The recurrence 
               was found by C. L. Mallows.
%D A003312 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003312 "Sieves", Popular Computing (Calabasas, CA), Vol. 2 (No. 13, Apr 1974), 
               pp. 6-7; sieve #5.
%D A003312 Solution to Problem 170, Popular Computing (Calabasas, CA), Vol. 5 (No. 
               51, Jun 1977), pp. 17.
%H A003312 T. D. Noe, <a href="b003312.txt">Table of n, a(n) for n=1..500</a>
%H A003312 <a href="Sindx_Si.html#sieve">Index entries for sequences generated by 
               sieves</a>
%e A003312 The first few sieving stages are as follows:
%e A003312 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
%e A003312 3 4 5 X 7 8 X 10 11 XX 13 14 XX 16 17 XX 19 20 ...
%e A003312 3 4 5 X 7 X X 10 11 XX XX 14 XX 16 XX XX 19 20 ...
%e A003312 3 4 5 X 7 X X 10 XX XX XX 14 XX 16 XX XX XX 20 ...
%e A003312 3 4 5 X 7 X X 10 XX XX XX 14 XX XX XX XX XX 20 ...
%p A003312 f:=proc(n) option remember; if n=1 then RETURN(3) fi; f(n-1)+floor( (f(n-1)-1)/
               2 ); end;
%Y A003312 Cf. A003309, A003310, A100464, A100562, A006999, A061418, A070885, A003311.
%Y A003312 Sequence in context: A030502 A073957 A162311 this_sequence A022440 A088130 
               A046840
%Y A003312 Adjacent sequences: A003309 A003310 A003311 this_sequence A003313 A003314 
               A003315
%K A003312 nonn,easy,nice
%O A003312 1,1
%A A003312 N. J. A. Sloane (njas(AT)research.att.com).
%E A003312 Entry revised Dec 01 2004