[seqfan] Re: A016910 (6n)^2 and twin primes
Olivier Gerard
olivier.gerard at gmail.com
Sun Jun 15 12:36:16 CEST 2014
=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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