A389544 a(n) is the smallest integer greater than a(n-1) such that all consecutive products in a(1)..a(n) are distinct, with a(1) = 2.

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset

1,1

Comments

Greedy sequence corresponding to the 421st Erdős Problem.

Links

Touch Sungkawichai, Table of n, a(n) for n = 1..20000

Thomas F. Bloom, Erdős Problem #421

Prog

(Python)
from itertools import count, islice
def A389544_gen(): # generator of terms
    an, conP, endP = 2, {1, 2}, {1, 2} # an; set of all consecutive/ending products resp.
    while True:
        yield an
        an = next(k for k in count(an+1) if k not in conP and all(k*p not in conP for p in endP))
        endP = {an} | {an*p for p in endP}
        conP |= endP
print(list(islice(A389544_gen(), 68))) # Michael S. Branicky, Jan 04 2026

Crossrefs

Cf. A001055, A333559, A390848 (complement), A392241.

Sequence in context: A098767 A333559 A153381 * A307750 A356734 A319630

Adjacent sequences: A389541 A389542 A389543 * A389545 A389546 A389547

Keyword

nonn,nice

Author

Touch Sungkawichai, Jan 02 2026

Status

approved