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A100464
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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.
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8
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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
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history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #3. [Annotated and scanned copy]
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EXAMPLE
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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 ...
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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