A100464 Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off and cross off all the numbers i*M + 1 for i >= 1. Repeat. The numbers that are left form the sequence.

3, 5, 8, 12, 14, 18, 20, 23, 27, 30, 32, 35, 38, 42, 44, 48, 50, 53, 59, 62, 68, 72, 74, 78, 80, 83, 87, 90, 92, 95, 98, 102, 104, 108, 110, 114, 117, 120, 122, 128, 132, 134, 138, 140, 143, 147, 150, 152, 158, 164, 168, 170, 173, 179, 182, 188, 192

Offset: 1

Author

N. J. A. Sloane, Nov 23 2004

Keywords

• nonn

Comments

Equivalently, each term is the lowest natural number n such that n mod k is not 1 for any number k in the sequence so far. Also, the average difference between terms grows as O(2 log log n). - Trevor Cappallo, Sep 10 2019

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 XX 12 XX 14 15 XX 17 18 XX 20 ...
3 X 5 X X 8 X XX XX 12 XX 14 15 XX XX 18 XX 20 ...
3 X 5 X X 8 X XX XX 12 XX 14 XX XX XX 18 XX 20 ...
		

Links

• Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #3. [Annotated and scanned copy]
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003309, A003310.