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. (Formerly M2436)

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

1,1

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

Example

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 ...

Prog

(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

Crossrefs

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

Sequence in context: A335860 A207038 A081401 * A108279 A002821 A046992

Adjacent sequences: A003308 A003309 A003310 * A003312 A003313 A003314

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Entry revised Nov 29 2004

Status

approved