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A285039 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. 3

%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

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)