A349227 Lexicographically earliest sequence of positive integers such that the product 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

1,4

Comments

This sequence has similarities with A088177; here we consider products of three consecutive terms, there products of two consecutive terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

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

Prog

(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)))
(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

Crossrefs

Cf. A088177, A349228.

Sequence in context: A071455 A288724 A198862 * A264025 A139465 A010244

Adjacent sequences: A349224 A349225 A349226 * A349228 A349229 A349230

Keyword

nonn

Author

Rémy Sigrist, Nov 11 2021

Status

approved