A138612 Permutation of natural numbers generated with the sieve algorithm described in the comment lines.

1, 2, 4, 3, 7, 12, 5, 11, 19, 28, 6, 15, 26, 39, 53, 8, 20, 35, 52, 71, 91, 9, 23, 42, 64, 88, 114, 141, 10, 27, 49, 76, 106, 138, 172, 207, 13, 33, 60, 93, 129, 168, 210, 253, 297, 14, 37, 68, 105, 148, 194, 243, 294, 347, 401, 16, 43, 79, 122, 171, 225, 282, 342

Offset: 1

Author

Ctibor O. Zizka, May 14 2008

Keywords

• nonn
• tabl

Comments

Sieve proceeds as:

1) take the 1st element from natural numbers (A000027): 1; remaining set is 2,3,4,5,6,7,8,9,10,...; S1={1}

2) take the 1st element from the remaining set: 2; remaining set is 3,4,5,6,7,8,9,10,...; take the 2nd element from the remaining set: 4; remaining set is 3,5,6,7,8,9,10,...; S2={2,4}

3) take the 1st element from the remaining set: 3; remaining set is 5,6,7,8,9,10,...; take the 3rd element from the remaining set: 7; remaining set is 5,6,8,9,10,11,12,...; take the 7th 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 1st element from the remaining set: 5; remaining set is 6,8,9,10,11,13,14,15,16,17,18,19,20,..; take the 5th element from the remaining set: 11; remaining set is 6,8,9,10,13,14,15,16,17,18,19,20,..; take the 11th element from the remaining set: 19; remaining set is 6,8,9,10,13,14,15,16,17,18,20,..; take the 19th 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.

Links

• A. Karttunen, Table of n, a(n) for n = 1..5050
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A166017. Left edge A166018, Right edge: A166019, Row sums: A166020. Cf. A138606-A138609.

Extensions

Edited, extended, keyword tabl and Scheme-code added by Antti Karttunen, Oct 05 2009