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A330531 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by 6.

%I A330531 #11 Dec 18 2019 14:31:58
%S A330531 1,6,2,3,4,9,8,12,5,18,7,24,10,15,14,21,16,27,20,30,11,36,13,42,17,48,
%T A330531 19,54,22,33,26,39,28,45,32,51,34,57,38,60,23,66,25,72,29,78,31,84,35,
%U A330531 90,37,96,40,63,44,69,46,75,50,81,52,87,56,93,58,99,62
%N A330531 Lexicographically earliest sequence of distinct positive integers such that the product of two consecutive terms is always divisible by 6.
%C A330531 This sequence is a permutation of the natural numbers with inverse A330577.
%C A330531 Apparently:
%C A330531 - for m > 1, the m-th run of consecutive terms such that gcd(6, a(n)) = 1 or 6 has 4*m-3 terms,
%C A330531 - for m > 1, the m-th run of consecutive terms such that gcd(6, a(n)) = 2 or 3 has 4*m-1 terms.
%H A330531 Rémy Sigrist, <a href="/A330531/b330531.txt">Table of n, a(n) for n = 1..10000</a>
%H A330531 Rémy Sigrist, <a href="/A330531/a330531.png">Colored scatterplot of the first 10000 terms</a>
%H A330531 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A330531 The first terms, alongside their product with the next term, are:
%e A330531   n   a(n)  a(n)*a(n+1)
%e A330531   --  ----  -----------
%e A330531    1     1            6
%e A330531    2     6           12
%e A330531    3     2            6
%e A330531    4     3           12
%e A330531    5     4           36
%e A330531    6     9           72
%e A330531    7     8           96
%e A330531    8    12           60
%e A330531    9     5           90
%e A330531   10    18          126
%o A330531 (PARI) s=0; v=1; for (n=1, 10 000, print (n " " v); s+=2^v; for (w=1, oo, if (!bittest(s,w) && (v*w)%6==0, v=w; break)))
%Y A330531 See A330530 for a similar sequence and additional comments.
%Y A330531 Cf. A330577 (inverse).
%K A330531 nonn
%O A330531 1,2
%A A330531 _Rémy Sigrist_, Dec 17 2019