[seqfan] Re: A016910 (6n)^2 and twin primes

[Tw Mike]

I'm trying to add the solutions to OEIS, see draft/A235644 , not sure if
the data 1, 2, 2, 5, 5, 3, 6, 3, 6,  .... is correct.
Yours mike,


2014-06-15 18:36 GMT+08:00 Olivier Gerard <olivier.gerard at gmail.com>:

> =On Sat, Jun 14, 2014 at 4:47 PM, Tw Mike <mt.kongtong at gmail.com> wrote:
>
> > Dear seqfans,
> >
> > It is conjectured that  A016910(n) = p_1 + p_2 + p_3 + p_4, where (p_1,
> > p_2) and (p_3, p_4) are twin prime pairs.
> >
> >
> Let us be clear. Either you conjecture this by yourself, and you should say
> so or
> you read about someone else conjecturing and you should give the source.
>
>  For example:  A016910(1) = 36 = 5 + 7 + 11 + 13.
> >
>
> Also you should check as much as possible before reporting it.
>
> In general, there seems to be many solutions for each n.
>
> For instance, before writing this email, I checked up to n=40 that there
> was at least one solution for each n, I looked into the sequence of the
> number of solutions
> to check if it was recorded in the OEIS (it is not), etc.
>
>
> > Are there some research or paper or progress of this conjecture?
> >
> >
> As Giovanni already said, what your are discussing implies that there is
> infinitely many twin primes.
> You might read papers about this unsolved problem and also papers on
> representations
> of numbers by sums of primes, a very active topic, related to the Goldberg
> conjecture and
> its variants.
>
> Olivier
>
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