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

[Charles Greathouse]

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.
>
> Franklin T. Adams-Watters
>
> -----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