A356873 a(n) is the smallest number k such that 2^k+1 has at least n distinct prime factors.

0, 5, 14, 18, 30, 42, 78, 78, 78, 90, 150, 150, 210, 210, 234, 234, 270, 390, 390, 390, 390, 450, 510, 630, 630, 630, 810, 810, 810, 966, 966, 1170, 1170, 1170, 1170, 1170, 1170, 1170

Offset

1,2

Comments

From Jon E. Schoenfield, Sep 04 2022: (Start)

a(39) <= a(40) <= a(41) <= 1530.

a(42) <= a(43) <= a(44) <= 1890.

a(45) <= a(46) <= 2070.

a(47) <= a(48) <= ... <= a(54) = 2730. (End)

Links

Table of n, a(n) for n=1..38.

Mathematica

a[n_] := Block[{k=0}, While[ Length@ FactorInteger[2^k + 1] < n, k++]; k]; Array[a, 12] (* Giovanni Resta, Oct 13 2022 *)

Prog

(Python)
from sympy import factorint, isprime
from itertools import count, islice
def f(n): return 1 if isprime(n) else len(factorint(n))
def agen():
    n = 1
    for k in count(0):
        v = f(2**k+1)
        while v >= n: yield k; n += 1
print(list(islice(agen(), 10))) # Michael S. Branicky, Sep 02 2022
(PARI) a(n) = my(k=1); while (omega(2^k+1) < n, k++); k; \\ Michel Marcus, Sep 05 2022

Crossrefs

Cf. A046799, A071852.

Cf. A180278, A219108, A356872.

Sequence in context: A053782 A296692 A102884 * A071852 A275809 A227793

Adjacent sequences: A356870 A356871 A356872 * A356874 A356875 A356876

Keyword

nonn,hard,more

Author

Alex Ratushnyak, Sep 02 2022

Extensions

a(11)-a(38) from Michael S. Branicky, Sep 02 2022 using A071852

Status

approved