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

On 8/28/25 2:15 PM, Ruud H.G. van Tol wrote:
> 
> On 2025-08-28 13:48, [email protected] 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