# [seqfan] Re: Generalizing Dirichlet, new sequences.

Neil Sloane njasloane at gmail.com
Wed Nov 30 21:18:27 CET 2016

```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.
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.
>

```