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

[Charles Greathouse]

688, 1552, 3496, 4360, 5008, 6352, 6952, 7546, 7672, 9256, 9625, 9712,
10062, 10300, 10840, 11632, 11875, 12112, 12136, 12460, 12712, 13432,
13648, 13744, 13912, 14152, 14812, 14920, 15484, 16562, 17050, 17104,
17272, 17608, 17752, 18130, 18232, 18616, 18952, 19062, 19624, 19792,
21100, 21136, 21352, 21640, 21976, 22990, 23125, 23292, 23368, 24232,
24867, 25012, 25112, 25420, 25564, 25712, 26032, 26512

It took about 10 seconds to generate 10,000 terms with a naive script. A
faster script, generating the 5-primes rather than factoring, would be much
faster.


Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Tue, Jan 29, 2013 at 10:59 PM, Jonathan Post <jvospost3 at gmail.com> wrote:

> 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.
>
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