A349227 Lexicographically earliest sequence of positive integers such that the products of three consecutive terms are all distinct.
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, 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, 9, 3, 3, 11, 1, 7, 7, 2, 11, 4, 3, 9, 6, 4, 6, 7, 6, 7
Offset: 1
Keywords
Examples
The first terms, alongside a(n)*a(n+1)*a(n+2), are: n a(n) a(n)*a(n+1)*a(n+2) -- ---- ------------------ 1 1 1 2 1 2 3 1 4 4 2 8 5 2 12 6 2 6 7 3 3 8 1 5 9 1 10 10 5 20
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
Programs
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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)))
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Python
def aupton(terms): alst, pset = [1, 1], set() for n in range(3, terms+1): p = p2 = alst[-1]*alst[-2] while p in pset: p += p2 alst.append(p//p2); pset.add(p) return alst print(aupton(86)) # Michael S. Branicky, Nov 12 2021
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