[seqfan] Re: On the divisibility of a certain linear recurrence

[Hugo Pfoertner]

Peter,

(OT) the SeqFan Archives are still broken, at least partially. IIRC, there
had been a statement (last year?) from Olivier that an attempt of a repair
will be made, but the problem seems to be permanent.

A target for Robert's comments could either be https://oeis.org/A015525 or
the new https://oeis.org/A323354 (Odd n such that A015525 is not
squarefree). I made this sequence, because it is a candidate for the
notorious "what comes next" question : 5, 15, 25, 35, 45, ?

You said: ... I suspected that I would see primes... There are a few:
https://oeis.org/A323353

Regards
Hugo

On Fri, Jan 11, 2019 at 12:34 PM Peter Luschny <peter.luschny at gmail.com>
wrote:

> John> a(3)=3*a(2) + 8*a(1) = 3*3 + 8*1 = 17, right? Why 9?
>
> Sloppy notation, missing 'for n >= 3' in my definition, the
> quantification is implicit. Works like Mathematica's
> LinearRecurrence[{3, 8}, {1, 3, 9}].
>
> Hugo> I've checked through p=157 and didn't find a counterexample.
>
> Thanks, of course I also checked a couple of values before asking.
> But it's quite clear that this route cannot lead to insight.
>
> > If not, the usual objection against making sequences using arbitrary
> > parameters might not apply and we could create at least 3 sequences,
>
> Of course you are free to submit such sequences, but it does
> not fit my way of thinking.
>
> Robert> This is somewhat reminiscent of Fibonacci-Wieferich
> primes (or Wall-Sun-Sun primes).
>
> Yes, it's part of an subject area that I couldn't even name yet.
> In fact, in the half second before I started to reflect and
> before I had seen any values, I suspected that I would see
> primes. Well, I guess squarefree numbers is also nice ...
>
> Robert> There are no more primes p < 1200000 with p^2 | a(N(p)).
>
> Please add this and other parts of your comment to the sequence.
>
> Thanks to all!
> Peter
>
> Off topic: This is what my browser shows me when I look at
> the seqfan archive page: http://luschny.de/temp/SeqfanArchive.jpg
> It does not show my original post, not John's post and not
> Hugo's post. I only learned about these posts since they were
> attached to Robert's post. What's going wrong here?
>
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