[seqfan] Re: Computing more terms of draft sequence A343745

[Alex Hall]

I downloaded the irregular primes up to 2 billion from
https://web.maths.unsw.edu.au/~davidharvey/index.php?page=research

Then I searched for pairs in it with this Python code:

with open("/home/alex/Downloads/twobillion/indices.txt") as f:
    for line in f:
        p, *indices = map(int, line.split())
        if any(a + 2 == b for a, b in zip(indices, indices[1:])):
            print(p, indices)

The only thing it printed was:

491 [292, 336, 338]
587 [90, 92]

How did you get those other primes? What are the indices and Bernoulli
numbers corresponding to 37?

On Sat, May 1, 2021 at 1:18 AM <rgwv at rgwv.com> wrote:

> In the order in which they appear: 587, 491, 37, 103, 59, 131, 67, 283,
> 101,
> 691, 157, 617, 593, 149, 233, 683, 271.
>
> If I understand the sequence properly.
>
> -----Original Message-----
> From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Felix Fröhlich
> Sent: Friday, April 30, 2021 4:24 PM
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Computing more terms of draft sequence A343745
>
> Dear SeqFans,
>
> I recently submitted A343745, which is still in draft mode. The name is
> "Consecutive irregular pairs, i.e., primes p where an integer k exists such
> that p divides the numerators of the Bernoulli numbers B_{2k} and
> B_{2k+2}."
>
> The paper by Johnson lists only the two terms currently in the data of the
> sequence, 491 and 587. Johnson states he searched to 30000. I think I am
> unable to extend the search bound myself. Can someone find a third term?
>
> Best regards
>
> Felix
>
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