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

Olivier Gerard olivier.gerard at gmail.com
Wed Jan 30 08:44:59 CET 2013


Please note that Paolo Lava and Georgi Guninski have also quickly proposed
programs and as many or more terms for this sequence.

Thanks for their reactivity and their desire to help.

Olivier



On Wed, Jan 30, 2013 at 8:03 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> 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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> >
>
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