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

[Max Alekseyev]

On Sat, Mar 13, 2010 at 5:38 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?

That's equivalent to Goldbach conjecture.
http://en.wikipedia.org/wiki/Goldbach_conjecture

>
> 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.

In other words, 2n = (n-m) + (n+m) is the sum of two primes.
Vice versa, if 2n = p + q then we can take m = (p-q)/2.

Max