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A345872 Lexicographically earliest sequence of positive integers such that the values A345415(a(n), a(n+1)) are all distinct.

%I A345872 #9 Jul 02 2021 03:34:48
%S A345872 1,1,2,3,5,7,5,8,11,13,11,18,23,13,15,13,21,19,21,23,18,31,19,30,37,
%T A345872 30,41,39,23,25,34,43,28,43,41,43,45,37,35,37,50,47,38,41,54,61,52,61,
%U A345872 59,57,55,53,64,53,70,53,76,37,69,49,66,73,71,69,71,73,75
%N A345872 Lexicographically earliest sequence of positive integers such that the values A345415(a(n), a(n+1)) are all distinct.
%C A345872 When writing gcd(a(n), a(n+1)) as u*a(n) + v*a(n+1) where u, v are minimal, the u's are all distinct.
%H A345872 Rémy Sigrist, <a href="/A345872/b345872.txt">Table of n, a(n) for n = 1..10000</a>
%H A345872 Rémy Sigrist, <a href="/A345872/a345872.gp.txt">PARI program for A345872</a>
%e A345872 The table A345415(n, k) begins:
%e A345872   n\k|  1  2   3   4
%e A345872   ---+--------------
%e A345872     1|  0  1   1   1
%e A345872     2|  0  0  -1   1
%e A345872     2|  0  1   0  -1
%e A345872     2|  0  0   1   0
%e A345872 For n = 1:
%e A345872 - we can choose a(1) = 1.
%e A345872 For n = 2:
%e A345872 - we can choose a(2) = 1,
%e A345872 - A345415(a(1), a(2)) = 0.
%e A345872 For n = 3:
%e A345872 - a(3) must be different from 1,
%e A345872 - we can choose a(3) = 2,
%e A345872 - A345415(a(2), a(3)) = 1.
%e A345872 For n = 4:
%e A345872 - a(4) must be different from 1 and from 2,
%e A345872 - we can choose a(4) = 3.
%o A345872 (PARI) See Links section.
%Y A345872 Cf. A345415, A345873.
%K A345872 nonn
%O A345872 1,3
%A A345872 _Rémy Sigrist_, Jun 27 2021