[seqfan] Re: Numbers that can be represented as 2p + 3q, where p and q are prime

Charles Greathouse charles.greathouse at case.edu
Tue Dec 4 22:37:04 CET 2012

```Also, to get the result I mentioned it would suffice to have the
result true for 'most' numbers -- no more than O(x/log^2 x)
exceptions. I think this is within current technology, even if the
main result is not.

Am I wrong here, too?

Charles

On 12/4/12, Charles Greathouse <charles.greathouse at case.edu> wrote:
> I realized that shortly after posting -- this is probably a
> Goldbach-like problem. I wonder if that might mean there are explicit
> references somewhere in the literature to add to the sequence?
>
> Charles
>
> On 12/4/12, franktaw at netscape.net <franktaw at netscape.net> wrote:
>> Considering that  similar questions about numbers of the form p + q are
>> still unsolved, I doubt you'll be able to solve this at this time.
>>
>>
>> -----Original Message-----
>> From: Charles Greathouse <charles.greathouse at case.edu>
>>
>> Almost a decade ago Randy Ekl submitted A079026, Numbers that can be
>> represented as 2p + 3q, where p and q are prime. Zak submitted a
>> b-file recently, which drew my attention to the sequence.
>>
>> It seems that all numbers n > 17 with gcd(n, 6) = 1 are members of
>> this sequence, in which case there are x/3 + 3x/(2 log x) + O(x/log^2
>> x) members of this sequence up to x: the only members of this sequence
>>> 30 which aren't coprime to 6 are those which are 4, 6, or 9 greater
>> than a prime.
>>
>> Any ideas on how to show that this is true?
>>
>> Of course any results in this direction would imply a formula for
>> A219955 as well.
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
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>
>
> --
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>

--
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
```