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
Programs
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Mathematica
a[n_] := Block[{k=0}, While[ Length@ FactorInteger[2^k + 1] < n, k++]; k]; Array[a, 12] (* Giovanni Resta, Oct 13 2022 *) -
PARI
a(n) = my(k=1); while (omega(2^k+1) < n, k++); k; \\ Michel Marcus, Sep 05 2022
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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
Extensions
a(11)-a(38) from Michael S. Branicky, Sep 02 2022 using A071852
Comments