[seqfan] Re: New sequence

M. F. Hasler seqfan at hasler.fr
Thu Apr 6 02:10:52 CEST 2017

On Wed, Apr 5, 2017 at 5:22 PM, Graeme McRae <graememcrae at gmail.com> wrote:

> for all possible primes p1, p2 such that p1+p2=E,
> neither E+p1 nor E+p2 is prime.
> 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 submitted https://oeis.org/draft/A284919
including PARI code based on Charles' proposal,
but not Graeme McRae's comment on the probably finite "for all" (or: no...)
(cf below: you are invited to add it, conveniently rephrased).
I also chose to include the two initial terms 0 and 2 which may be arguable
but may affect search results only in a positive sense.

Looking at other Goldbach related sequences, they often use n where E=2n,
so I wonder whether the sequence a(n)/2 should also be submitted.

> 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.

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