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A349227 Lexicographically earliest sequence of positive integers such that the products of three consecutive terms are all distinct.

%I A349227 #12 Aug 29 2024 17:13:49
%S A349227 1,1,1,2,2,2,3,1,1,5,2,2,4,3,3,1,5,5,2,3,3,3,5,4,2,4,6,3,3,7,1,1,11,2,
%T A349227 2,7,1,5,11,2,3,7,4,2,8,5,3,5,6,5,6,7,3,5,9,5,6,8,2,7,5,4,5,8,5,7,5,7,
%U A349227 9,3,3,11,1,7,7,2,11,4,3,9,6,4,6,7,6,7
%N A349227 Lexicographically earliest sequence of positive integers such that the products of three consecutive terms are all distinct.
%C A349227 This sequence has similarities with A088177; here we consider products of three consecutive terms, there products of two consecutive terms.
%H A349227 Rémy Sigrist, <a href="/A349227/b349227.txt">Table of n, a(n) for n = 1..10000</a>
%e A349227 The first terms, alongside a(n)*a(n+1)*a(n+2), are:
%e A349227   n   a(n)  a(n)*a(n+1)*a(n+2)
%e A349227   --  ----  ------------------
%e A349227    1     1                   1
%e A349227    2     1                   2
%e A349227    3     1                   4
%e A349227    4     2                   8
%e A349227    5     2                  12
%e A349227    6     2                   6
%e A349227    7     3                   3
%e A349227    8     1                   5
%e A349227    9     1                  10
%e A349227   10     5                  20
%o A349227 (PARI) s=0; pp=p=1; for (n=1, 86, for (v=1, oo, if (!bittest(s, q=pp*p*v), print1 (pp", "); s+=2^q; pp=p; p=v; break)))
%o A349227 (Python)
%o A349227 def aupton(terms):
%o A349227     alst, pset = [1, 1], set()
%o A349227     for n in range(3, terms+1):
%o A349227         p = p2 = alst[-1]*alst[-2]
%o A349227         while p in pset: p += p2
%o A349227         alst.append(p//p2); pset.add(p)
%o A349227     return alst
%o A349227 print(aupton(86)) # _Michael S. Branicky_, Nov 12 2021
%Y A349227 Cf. A088177, A349228.
%K A349227 nonn
%O A349227 1,4
%A A349227 _Rémy Sigrist_, Nov 11 2021