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

1,2

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

Prog

(MIT Scheme:)
(define (A138612 n) (if (< n 3) n (let loop ((k (if (zero? (A002262 (-1+ n))) 1 (A138612 (-1+ n)))) (i 1)) (cond ((not-lte? (A166017 i) (-1+ n)) (if (= 1 k) i (loop (-1+ k) (1+ i)))) (else (loop k (1+ i)))))))
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

Crossrefs

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

Sequence in context: A238953 A238964 A035507 * A246680 A294244 A333028

Adjacent sequences: A138609 A138610 A138611 * A138613 A138614 A138615

Keyword

nonn,tabl

Author

Ctibor O. Zizka, May 14 2008

Extensions

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

Status

approved