[seqfan] Re: Next terms?

Harvey P. Dale hpd at hpdale.org
Wed May 24 14:26:11 CEST 2017

```Peter:
I understand. This rule generates all of the terms of the sequence: primes p such that p+6, p+12, p+18, p+20, p+26, p+32, and p+38 are all primes.
Best,
Harvey

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Peter Munn
Sent: Tuesday, May 23, 2017 5:18 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Next terms?

Hello Harvey,

By "a pattern ... including ... a pattern" I meant that extra primes are allowed within the pattern.  So 41 qualifies even though 43 and 71 are additional to the pattern that continues 47, 53, 59, 61, 67, 73, 79.

I suspect, however, that I may be missing a condition for the sequence, as none of Zak's values are congruent to 251 mod 330. This condition may, perhaps, take the form of (a(n)+k)/m being prime for some specified values of k and m.

Best Regards.  Peter

On Tue, 23 May, 2017 2:41 pm, Harvey P. Dale wrote:
> 	The terms, with 3 exceptions, do fit Peter's model, but the terms 41,
> 1464251, and 68632121 do not. The next two terms to fit Peter's model
> are
> 122898851 and 164527151.
> 	Best,
> 	Harvey
>
> -----Original Message-----
> From: SeqFan On Behalf Of zak seidov via SeqFan
> Sent: Monday, May 22, 2017 2:27 AM

> Peter,As I vaguely recollect
> you are (very?) close to the clue.Zak
>
>       From: Peter Munn <techsubs at pearceneptune.co.uk>
>  Sent: Monday, May 22, 2017 7:41 AM
>
> On Sun, 21 May, 2017 11:45 am, zak seidov via SeqFan wrote:
>> {41, 344231, 1464251, 9646271, 48691151, 53544461, 58182011,
>> 68632121, 74656931, 74752571, 92195381}.
>> Next terms?I don't know.
>> I found it in my old archiveÂ  - no code and no explanation...Zak
>
> It looks like p begins a pattern of primes including a symmetrical
> pattern of eight primes centred on a prime pair with the other six at
> intervals of 6.

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