A003311 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.

3, 5, 8, 11, 15, 18, 23, 27, 32, 38, 42, 47, 53, 57, 63, 71, 75, 78, 90, 93, 98, 105, 113, 117, 123, 132, 137, 140, 147, 161, 165, 168, 176, 183, 188, 197, 206, 212, 215, 227, 233, 237, 243, 252, 258, 267, 278, 282, 287, 293, 303, 312, 317, 323

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			The first few sieving stages are as follows:
  3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
  3 X 5 6 X 8 9 XX 11 12 XX 14 15 XX 17 18 XX 20 ...
  3 X 5 X X 8 9 XX 11 12 XX XX 15 XX 17 18 XX 20 ...
  3 X 5 X X 8 X XX 11 12 XX XX 15 XX 17 18 XX 20 ...
  3 X 5 X X 8 X XX 11 XX XX XX 15 XX 17 18 XX 20 ...
  3 X 5 X X 8 X XX 11 XX XX XX 15 XX XX 18 XX 20 ...
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Popular Computing (Calabasas, CA), Sieves: Problem 43, 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]
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003309, A003310, A100464, A003312, A100562, A100585, A052548.

Programs

Haskell

a003311 n = a003311_list !! (n-1)
a003311_list = f [3..] where
   f (x:xs) = x : f (g xs) where
     g zs = us ++ g vs where (_:us, vs) = splitAt x zs
-- Reinhard Zumkeller, Nov 12 2014

Extensions

Entry revised Nov 29 2004