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%I #14 Feb 19 2018 14:45:49
%S 1,2,3,4,5,6,7,8,9,10,11,15,12,13,18,14,16,17,21,20,19,24,22,23,27,26,
%T 25,30,28,29,40,31,33,32,34,35,36,37,48,38,39,42,41,52,43,56,44,45,46,
%U 47,60,49,64,50,51,54,53,80,55,57,58,59,68,61,72,62,63
%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 1, if prime(k) is the least prime factor of a(n) then k divides a(n+1) (where prime(k) denotes the k-th prime).
%C In other words, for any n > 1, A055396(a(n)) divides a(n+1).
%C This sequence has similarities with A285039 (especially visually).
%C See also A299442 for the variant involving greatest prime factors.
%C This sequence is a permutation of the natural numbers, with inverse A299703:
%C - for any n > 1, if a(n) is odd, then lpf(a(n+1)) < lpf(a(n)), and a(n+k) will be even for some k > 0 (where lpf = A020639),
%C - hence we have infinitely many even terms,
%C - and as after an even term, we can choose the least positive number not yet in the sequence, eventually every positive number will appear.
%H Rémy Sigrist, <a href="/A299441/b299441.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A299441/a299441.gp.txt">PARI program for A299441</a>
%H Rémy Sigrist, <a href="/A299441/a299441.png">Scatterplot of (n, a(n)-1) for n=1..1000000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside A055396(a(n)), are:
%e n a(n) A055396(a(n))
%e -- ---- -------------
%e 1 1 0
%e 2 2 1
%e 3 3 2
%e 4 4 1
%e 5 5 3
%e 6 6 1
%e 7 7 4
%e 8 8 1
%e 9 9 2
%e 10 10 1
%e 11 11 5
%e 12 15 2
%e 13 12 1
%e 14 13 6
%e 15 18 1
%e 16 14 1
%e 17 16 1
%e 18 17 7
%e 19 21 2
%e 20 20 1
%o (PARI) See Links section.
%Y Cf. A020639, A055396, A285039, A299442, A299703 (inverse).
%K nonn
%O 1,2
%A _Rémy Sigrist_, Feb 10 2018