[seqfan] Searching for "Sophie Germain 5-almost primes"

[Jonathan Post]

By hand, I found what may be the smallest "Sophie Germain 5-almost
prime" -- namely an integer N with exactly 5 prime factors (not
necessarily distinct) such that 2N+1 also has exactly 5 prime factors:

688 = 2^4 * 43

2*688 + 1 = 1377 = 3^4 * 17

There are no other such N < 1000.

It would be worth sharing authorship with whomever could generate
three rows worth of the next such values, by analogy with
A111153	Sophie Germain semiprimes: semiprimes n such that 2n+1 is also
a semiprime.
A111173	Sophie Germain 3-almost primes.
A111176	Sophie Germain 4-almost primes.