A392162 a(n) is the smallest number not yet in the sequence that has exactly one prime factor in common with a(n-1) and has at least two other different prime factors that are not factors of a(n-1); a(1) = 2.

2, 30, 154, 60, 182, 66, 70, 78, 105, 102, 110, 42, 130, 84, 165, 114, 140, 132, 170, 126, 190, 138, 195, 168, 220, 156, 230, 174, 231, 90, 238, 120, 266, 150, 273, 180, 286, 186, 255, 198, 260, 204, 280, 222, 285, 234, 290, 228, 308, 240

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(2) = 30 since it shares the prime 2 with a(1) = 2 and has two other different primes not contained in a(1) (3 and 5).
a(3) = 154 = 2*7*11 since it shares the prime 2 with a(2) = 30 and has two other different primes not contained in a(2) (7 and 11).

Prog

(Python)
from sympy import factorint
from functools import cache
from itertools import count, islice
@cache
def pf(n): return set(factorint(n))
def cond(pfan, pfk): return len(pfk&pfan) == 1 and len(pfk-pfan) >= 2
def agen():
    an, aset, m = 2, {2}, 3
    while True:
        yield an
        pfan = pf(an)
        m = next(k for k in count(m) if k not in aset and len(pf(k)) >= 3)
        an = next(k for k in count(m) if k not in aset and cond(pfan, pf(k)))
        aset.add(an)
print(list(islice(agen(), 55))) # Michael S. Branicky, Jan 06 2026

Crossrefs

Cf. A064413, A350352.

Sequence in context: A285991 A078838 A267851 * A379845 A089288 A232602

Adjacent sequences: A392159 A392160 A392161 * A392163 A392164 A392165

Keyword

nonn

Author

Enrique Navarrete, Jan 01 2026

Status

approved