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

[Charles Greathouse]

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