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%I #19 Oct 28 2020 18:03:53
%S 1,2,4,6,3,9,5,10,20,8,7,14,28,12,15,30,40,16,11,22,44,18,21,42,56,24,
%T 27,33,55,110,50,26,13,39,36,48,32,17,34,68,38,19,57,45,60,70,84,63,
%U 51,85,170,80,46,23,69,54,66,88,77,35,105,75,72,52,78,117
%N Lexicographically earliest infinite sequence of distinct positive numbers such that for any prime p, any run of consecutive multiples of p has length exactly 3.
%C If a prime p divides a(n), then there is a run of exactly three terms (one of which is a(n)) that are divisible by p.
%C If "three" is changed to "two", we get A280864.
%C Conjecture: This is a permutation of the positive integers.
%H Rémy Sigrist, <a href="/A338338/b338338.txt">Table of n, a(n) for n = 1..20000</a>
%H Rémy Sigrist, <a href="/A338338/a338338.gp.txt">PARI program for A338338</a>
%e After 1,2,4,6,3, we have had two successive multiples of 3, so the next term must be a multiple of 3 we have not yet seen, hence 9. The following term is then the smallest number not yet seen which is not a multiple of 3, hence 5.
%o (PARI) See Links section.
%Y A338339-A338349, A338440, A338449, A338450, and A338451 analyze this sequence from various points of view.
%Y Cf. A280864, A338441.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 27 2020
%E Corrected and extended by _Rémy Sigrist_, Oct 27 2020