%I #17 Jun 13 2021 03:24:09
%S 1,2,4,3,6,5,8,10,7,12,9,11,15,18,13,14,16,17,20,22,19,24,21,23,27,30,
%T 25,26,28,29,32,34,31,36,33,35,39,40,38,37,42,44,41,46,48,43,45,50,47,
%U 52,54,49,51,56,57,58,60,53,55,65,59,70,62,61,64,66,63
%N Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime.
%C In other words, for any n > 0, at least one of gcd(a(n), a(n+1)), gcd(a(n), a(n+2)), gcd(a(n+1), a(n+2)) is strictly greater than 1.
%C This sequence has connections with the Yellowstone permutation (A098550).
%C Conjecture: this sequence is a permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A338618/b338618.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A338618/a338618.gp.txt">PARI program for A338618</a>
%e The first terms, alongside associated GCD's, are:
%e n a(n) gcd(a(n),a(n+1)) gcd(a(n),a(n+2)) gcd(a(n+1),a(n+2))
%e -- ---- ---------------- ---------------- ------------------
%e 1 1 1 1 2
%e 2 2 2 1 1
%e 3 4 1 2 3
%e 4 3 3 1 1
%e 5 6 1 2 1
%e 6 5 1 5 2
%e 7 8 2 1 1
%e 8 10 1 2 1
%e 9 7 1 1 3
%e 10 12 3 1 1
%o (PARI) See Links section.
%Y See A338619 for a similar sequence.
%Y Cf. A084937, A098550.
%K nonn
%O 1,2
%A _Rémy Sigrist_, Nov 04 2020