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A138612 Permutation of natural numbers generated with the sieve algorithm described in the comment lines. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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 A296449

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

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)