Re: PARI/GP wrong on 7!!+7+1 being not prime, or oeis.org/Mathematica?

[Vincent Delecroix <vincent.delecroix@u-bordeaux.fr>]

On 8/28/25 2:15 PM, Ruud H.G. van Tol wrote:
> On 2025-08-28 13:48, hermann@stamm-wilbrandt.de wrote:
> > The sequence is:
> > https://oeis.org/search?q=5%2c7%2c13%2c113%20id:A118743
> > [...]
> > Is 7!!+7+1 prime or not?
> >
> > hermann@7950x:~$ gp -q
> > ? for(n=1,12,if(isprime(n!!+n+1),print(n,": ",n!!+n+1));print1("."))
> > 1: 3
> > .2: 5
> > ...........
> > ? ##
> >   ***   last result computed in 4min, 32,167 ms.
>
> If !! means "double factorial", then 1 is the only odd that can lead to 
> a prime:
> 3!! is even, plus 3 plus 1, is still even.
>
> So what does !! mean here?
> (see also the Maple code)

The n!! notation is rather standard in combinatorics, see eg

https://en.wikipedia.org/wiki/Double_factorial
Best
Vincent