[seqfan] Re: Generalizing Dirichlet, new sequences.

[Neil Sloane]

and if we also want p+3 to be 4 times a prime, the primes p are
12721, 16921, 19441, 24481, 49681, 61561, 104161, 229321, 255361, 259681,

    266401, 291721, 298201, 311041, 331921, 419401, 423481, 436801, 446881,

    471241, 525241, 532801, 539401, 581521, 600601, 663601, 704161, 709921,

    783721, 867001, 904801, 908041, 918361 ...

which will be A278584, A278585 for the two versions

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Nov 30, 2016 at 1:52 PM, rkg <rkg at ucalgary.ca> wrote:

> I didn't find 13, 37, 157, 541, 877, ... in OEIS.
> It is a subseq of A068228 = A141122. Nor did I find
> 12, 36, 156, 540, 876, ... These are the values of n
> for which n+1 is prime, n+2 is twice a prime and
> n+3 is thrice a prime.  The former sequence is
> primes p such that p+1 is twice a prime and p+2 is
> thrice a prime.  Presumably infinite, though I
> don't know what generalizations there are for
> Dirichlet's theorem on primes in arithmetic prograssions.
>
> I'm skating on thin ice -- see A045753, A002822.  R.
>