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%I M2436 #24 Oct 22 2023 00:14:25
%S 3,5,8,11,15,18,23,27,32,38,42,47,53,57,63,71,75,78,90,93,98,105,113,
%T 117,123,132,137,140,147,161,165,168,176,183,188,197,206,212,215,227,
%U 233,237,243,252,258,267,278,282,287,293,303,312,317,323
%N 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 the first, (M+1)st, (2M+1)st, (3M+1)st, etc. Repeat. The numbers that are left form the sequence.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Reinhard Zumkeller, <a href="/A003311/b003311.txt">Table of n, a(n) for n = 1..10000</a>
%H Popular Computing (Calabasas, CA), <a href="/A003309/a003309.pdf">Sieves: Problem 43</a>, Vol. 2 (No. 13, Apr 1974), pp. 6-7. Based on a misreading of Sieve #3. A100464 is the correct version. [Annotated and scanned copy]
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%e The first few sieving stages are as follows:
%e 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
%e 3 X 5 6 X 8 9 XX 11 12 XX 14 15 XX 17 18 XX 20 ...
%e 3 X 5 X X 8 9 XX 11 12 XX XX 15 XX 17 18 XX 20 ...
%e 3 X 5 X X 8 X XX 11 12 XX XX 15 XX 17 18 XX 20 ...
%e 3 X 5 X X 8 X XX 11 XX XX XX 15 XX 17 18 XX 20 ...
%e 3 X 5 X X 8 X XX 11 XX XX XX 15 XX XX 18 XX 20 ...
%o (Haskell)
%o a003311 n = a003311_list !! (n-1)
%o a003311_list = f [3..] where
%o f (x:xs) = x : f (g xs) where
%o g zs = us ++ g vs where (_:us, vs) = splitAt x zs
%o -- _Reinhard Zumkeller_, Nov 12 2014
%Y Cf. A003309, A003310, A100464, A003312, A100562, A100585, A052548.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Entry revised Nov 29 2004
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