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

[Peter Luschny]

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?