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A308058 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) * a(m+1)^2 <> a(n) * a(n+1)^2.

%I A308058 #15 Feb 13 2021 14:37:28
%S A308058 1,1,2,1,3,1,4,3,2,2,3,3,4,4,5,1,5,2,4,6,1,7,1,9,5,3,5,4,7,2,5,5,6,2,
%T A308058 6,3,6,4,8,4,9,7,3,7,4,10,1,11,1,13,1,17,1,19,1,22,1,23,1,24,3,8,5,7,
%U A308058 5,8,6,5,9,9,10,2,7,6,7,7,8,7,9,11,2,9,12
%N A308058 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) * a(m+1)^2 <> a(n) * a(n+1)^2.
%C A308058 This sequence has similarities with A088178; here we consider a(n)*a(n+1)^2, there we consider a(n)*a(n+1).
%H A308058 Rémy Sigrist, <a href="/A308058/b308058.txt">Table of n, a(n) for n = 1..10000</a>
%e A308058 The first terms, alongside a(n)*a(n+1)^2, are:
%e A308058   n   a(n)  a(n)*a(n+1)^2
%e A308058   --  ----  -------------
%e A308058    1     1              1
%e A308058    2     1              4
%e A308058    3     2              2
%e A308058    4     1              9
%e A308058    5     3              3
%e A308058    6     1             16
%e A308058    7     4             36
%e A308058    8     3             12
%e A308058    9     2              8
%e A308058   10     2             18
%o A308058 (PARI) s=0; v=1; for(n=1, 83, print1(v", "); for (w=1, oo, if (!bittest(s,x=v*w^2), s+=2^x; v=w; break)))
%Y A308058 See A308057 for an additive variant.
%Y A308058 Cf. A088178.
%K A308058 nonn
%O A308058 1,3
%A A308058 _Rémy Sigrist_, May 10 2019