[seqfan] Re: A (new) constant related to the Lucas-Lehmer-test. Is this worth an entry in OEIS?

Gottfried Helms helms at uni-kassel.de
Fri Apr 6 20:56:30 CEST 2012

Hi Maximilian -

Am 06.04.2012 16:41 schrieb Maximilian Hasler:
> For what it's worth, the explicit expression for the n-th term of the
> sequence (and the related constant) is well known since "ever", and
> various forms are given in A003010.

Thanks for that link; the references list as well as the comments look
much interesting.
> The interest of the test is that the computation **mod Mp** allows to
> decide about primality, the explicit terms themselves (without mod Mp)
> are of no practical interest in view of their size (note that not just
> the first 10, 100 or 1000 terms are needed, but at present one is
> interested in  n ~ Mp ~ 2^p with p ~ 5x10^7
> and a(n) = (2+sqrt(3))^(2^n)  would have 0.597 * 2^2^5e7 digits...

True, I'm aware of this. That's why I wrote, that the constant is
not useful for practical testing. But I find it a curious property.

> But this does not mean that such constants should not be added to OEIS
> which is still much less complete than Simon Plouffe's tables, btw
> 2+sqrt(3) = A019973 is already there since 1996 at least.
Yes, perhaps someone else plays around with the same idea and arrives
at the same number. Why not having the number in OEIS to link to
the comments. On the other hand: not every number need be in OEIS and
need be commented; there should be a sufficient degree of nontriviality.
So that's the reason for my asking for votes...

Kind regards -

Gottfried Helms

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