%I
%S 1,2,3,4,6,5,8,7,10,9,12,13,14,15,11,16,18,20,21,17,22,24,19,26,27,23,
%T 28,30,25,32,33,31,34,36,35,38,39,40,29,42,43,44,45,46,48,37,50,51,52,
%U 41,54,55,56,49,58,57,60,47,62,63,64,53,66,65,68,59,70
%N Lexicographically earliest sequence of distinct terms such that, for any n>0, a(n) is divisible by k and a(n+1) is divisible by prime(k) for some k.
%C As prime(1)=2, this sequence can always be extended with an even number.
%C This sequence is a permutation of the natural numbers, with inverse A285041 (say prime(k) divides n: the sequence contains all the multiples of 2*k, hence n will eventually be chosen).
%C This sequence has a fractal structure that is highlighted in the illustrations of some derived sequences in the Links section.
%H Rémy Sigrist, <a href="/A285039/b285039.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A285039/a285039.png">Scatterplot of a(n)n</a>
%H Rémy Sigrist, <a href="/A285039/a285039_2.png">Scatterplot of Sum_{k=1..n} (1)^a(n)</a>
%H Rémy Sigrist, <a href="/A285039/a285039.gp.txt">PARI program for A285039</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%Y Cf. A285041 (inverse).
%K nonn
%O 1,2
%A _Rémy Sigrist_, Apr 08 2017
