%I #6 Jan 05 2013 11:00:18
%S 3,11,13,2073601,146313215999,52563198423859200001,
%T 709885457731229765106401279999999,
%U 15120395453651827088974983182763034097693491200000000001
%N Primes of the form n!*(n+1)!*(n+2)! - 1 or n!*(n+1)!*(n+2)! + 1.
%C Primes of the form A010790(k)-1 or A010790(k)+1. This is the 3rd sequence in the supersequence whose first member is factorial primes, A002981 UNION A002982, and whose 2nd member is A176038 Primes of the form n!*(n+1)! - 1 or n!*(n+1)! + 1.
%C a(9) has already 486 digits and is not listed for that reason. The sequence is generated by the n-values 0, 1, 1, 4, 6, 9, 13, 19, 101, 196,... [From _R. J. Mathar_, Oct 03 2010]
%C a(9) also ends with 72 nines. - _Harvey P. Dale_, Jan 05 2013
%e a(2) = 11 because 1!*(1+1)!*(1+2)! - 1 = 11 is prime. a(4) = 2073601 because 4!*(4+1)!*(4+2)! + 1 = 2073601 is prime. a(7) because 13!*(13+1)!*(13+2)! - 1 = 709885457731229765106401279999999 is prime.
%t Select[Union[Flatten[Times@@#+{1,-1}&/@Partition[Range[0,30]!,3,1]]], PrimeQ] (* _Harvey P. Dale_, Jan 05 2013 *)
%Y Cf. A000040, A000142, A002981, A002982, A010790, A176038.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 07 2010
%E a(8) from _R. J. Mathar_, Oct 03 2010