[seqfan] Re: New sequence

Jamie Morken jmorken at shaw.ca
Thu Apr 13 03:56:57 CEST 2017

```Hi,I previously came across this sequence as a subset of A275768,it is the n values for A275768 where a(n) = 0 and n is congruent to 2,4 mod 6:
Here are the first few terms, they match A284919 except for missing n=0 and n=6.n a(n)2    0
4    0
28    0
38    0
52    0
58    0
62    0
68    0
74    0
80    0
82    0
88    0
94    0
98    0
112    0These two sequences are also related as they are congruent to 2,4 mod 6,but a(n) = 1 and a(n) = 2 instead.n a(n)14    1
22    1
26    1
32    1
34    1
40    1
44    1
46    1
64    1
86    1
92    1
104    1
106    1
110    1
116    1n a(n)8    2
10    2
16    2
20    2
50    2
56    2
70    2
76    2
100    2
160    2
170    2
176    2
196    2
226    2
230    2cheers,Jamie
>From :     M. F. Hasler <seqfan at hasler.fr>
Subject :     [seqfan] Re: New sequence
To :     Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

Wed, Apr 05, 2017 05:10 PM
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...)
version
(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.
--
Maximilian

> 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.
>From : M. F. Hasler <seqfan at hasler.fr>
Subject : [seqfan] Re: New sequence
To : Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

Wed, Apr 05, 2017 05:10 PM
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...)
version
(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.
--
Maximilian

> 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.

```