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

1,1

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

Links

Table of n, a(n) for n=1..57.

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

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 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 ...

Crossrefs

Cf. A003309, A003310.

Sequence in context: A289076 A372519 A342779 * A114891 A285953 A287380

Adjacent sequences: A100461 A100462 A100463 * A100465 A100466 A100467

Keyword

nonn

Author

N. J. A. Sloane, Nov 23 2004

Status

approved