%I #13 Jun 13 2022 15:44:45

%S 2,5,19,193,1801,56240459218944001,

%T 112873711099106889552388221969528619131820978659655680000000000001

%N Primes of the form n!*n!! + 1.

%C For n > 4, the last digits of the prime numbers are of the form 01, 001, 0000000000001,...,...000001.

%C Generated by n = 1, 2, 3, 4, 5, 14, 37, 48, 50, 52,... - R. J. Mathar, Dec 21 2011

%C The next term (a(8)) has 93 digits. - _Harvey P. Dale_, Jun 13 2022

%e 19 is in the sequence because, for n = 3, 3!*3!! + 1 = 6*3 + 1 = 19.

%t a={}; Do[p=n!*n!!+1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^3}]; Print[a];

%t Select[Table[n! n!!+1,{n,40}],PrimeQ] (* _Harvey P. Dale_, Jun 13 2022 *)

%Y Cf. A000142, A006882.

%K nonn

%O 1,1

%A _Michel Lagneau_, Dec 19 2011