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%I #9 Mar 10 2015 02:05:04
%S 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,
%T 114,141,10,27,49,76,106,138,172,207,13,33,60,93,129,168,210,253,297,
%U 14,37,68,105,148,194,243,294,347,401,16,43,79,122,171,225,282,342
%N Permutation of natural numbers generated with the sieve algorithm described in the comment lines.
%C Sieve proceeds as:
%C 1) take the 1st element from natural numbers (A000027): 1; remaining set is 2,3,4,5,6,7,8,9,10,...; S1={1}
%C 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}
%C 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}
%C 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,...;
%C thus S4={5,11,19,28}.
%C 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.
%H A. Karttunen, <a href="/A138612/b138612.txt">Table of n, a(n) for n = 1..5050</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (MIT Scheme:)
%o (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)))))))
%o (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
%Y Inverse: A166017. Left edge A166018, Right edge: A166019, Row sums: A166020. Cf. A138606-A138609.
%K nonn,tabl
%O 1,2
%A _Ctibor O. Zizka_, May 14 2008
%E Edited, extended, keyword tabl and Scheme-code added by _Antti Karttunen_, Oct 05 2009
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