[seqfan] Re: New sequence

[Graeme McRae]

I think the sequence Claudio is looking for is defined as follows:

E is in the sequence if, for all possible primes p1, p2 such that p1+p2=E,
neither E+p1 nor E+p2 is prime.

Claudio conjectured that the sequence is 4, 6, 28, 38, 52, 62, 68, 74, etc.

However, when I did the calculations, I found that 58 is also in the
sequence. The first few terms I found were:
4, 6, 28, 38, 52, 58, 62, 68, 74, 80, 82, 88, 94, 98, 112, 118, 122, 124,
128, 136...

I searched for it in OEIS, and did not find it.

I also looked for even numbers such that *all* the values E+pn are prime.
The only such even numbers I found smaller than 1000 were 8 and 12. In
fact, the only even numbers smaller than 1000 such that all but one of the
values E+pn are prime are 8, 12, 18, 24, and 30. I wonder if these
sequences are finite.