[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"!

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