# [seqfan] Re: finite a(n) for q=0 and infinite a(n) for q>0?

M. F. Hasler seqfan at hasler.fr
Thu Oct 25 01:34:02 CEST 2018

```On Wed, 24 Oct 2018, 15:57 <israel at math.ubc.ca> wrote:

> That there are infinitely many such primes is Polignac's conjecture.
>

Polignac's conjecture is more precisely about gaps, but here we don't
require that these are gaps (with no other primes in between).
Polignac's conjecture is relevant for A174350 <http://oeis.org/A174350>,
where row n lists the primes followed by a gap of 2n.
The first such is A000230 <https://oeis.org/A000230>(n) = A174350(n,1)  (i.e.,
column 1 of that table).
So,  A000230(q)+q is an upper limit for the k such that k +- q is prime.

But you should have a(0)=2 and a(1)=4, and then your sequence is A087711.
>

We all agree :-)

- Maximilian

On Oct 24 2018, Allan Wechsler wrote:
>
> >It is always my habit to look to see if all the simpler concepts than a
> >given proposal are already in the Encyclopedia. In this case, I have just
> >discovered that we seem to be missing "a(n) = smallest k such that k +/- n
> >are both prime"!

```