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

[apovolot at gmail.com]

Hello Olivier - then you could probably incorporate the following from A235644


REFERENCES	
Liang ding xiang, problem solving 93#, Bulletin of Mathematics (Wuhan), 6(1992),41. ISSN 0488-7395.


> On Jun 16, 2014, at 5:34 PM, Olivier Gerard <olivier.gerard at gmail.com> wrote:
> 
> Dear Mike,
> 
> This has already been done under https://oeis.org/A243941.
> 
> Olivier
> 
> 
> 
>> On Mon, Jun 16, 2014 at 1:24 PM, Tw Mike <mt.kongtong at gmail.com> wrote:
>> 
>> 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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