[seqfan] Re: No "-1" value in A047949?

[Maximilian Hasler]

On Sat, Mar 13, 2010 at 11:38 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> It looks to me as if no "-1" value is there in the first 10,000
> values.  Is that correct?  Is there a proof that no such value exists?
>
> A047949         a(2) = a(3) = 0; for n >= 4, a(n) = largest m such that n-m
> and n+m are both primes, or -1 if no such m exists.


This is Goldbach's conjecture, 2n = sum of 2 primes p+q
(p=n-m and q=n+m in the above notations),
see also A002372.

> What is a(n) asymptotically?

probably most terms are near the upper bound n-3,
but since one has no proof that a(n) "exists" (i.e. not = -1) for all n,
we can't hope to have an asymptotic expression valid for all
sufficiently large n.

Maximilian