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COMMENTS
| Sieve proceeds as:
1) take the 1-st element from natural numbers (A000027): 1; remaining set is 2,3,4,5,6,7,8,9,10,...; S1={1}
2) take the 1-st element from the remaining set: 2; remaining set is 3,4,5,6,7,8,9,10,...; take the 2-nd element from the remaining set: 4; remaining set is 3,5,6,7,8,9,10,...; S2={2,4}
3) take the 1-st element from the remaining set: 3; remaining set is 5,6,7,8,9,10,...; take the 3-rd element from the remaining set: 7; remaining set is 5,6,8,9,10,11,12,...; take the 7-th element from the remaining set: 12; remaining set is 5,6,8,9,10,11,13,14,15,16,17,18,19,20,..; S3={3,7,12}
4) take the 1-st element from the remaining set: 5; remaining set is 6,8,9,10,11,13,14,15,16,17,18,19,20,..; take the 5-th element from the remaining set: 11; remaining set is 6,8,9,10,13,14,15,16,17,18,19,20,..; take the 11-th element from the remaining set: 19; remaining set is 6,8,9,10,13,14,15,16,17,18,20,..; take the 19-th element from the remaining set: 28; remaining set is 6,8,9,10,13,14,15,16,17,18,20,21,22,23,24,25,26,27,29,30,31,...;
thus S4={5,11,19,28}.
The sequence is concatenation of such subsequences S1,S2,S3,S4,S5,...,Sn, ..., where each subsequence consists of n nondecreasing terms. Alternatively, these can be viewed as rows of a triangular table.
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