%I
%S 1,2,6,24,720,5040,39916800,479001600,87178291200,
%T 10888869450418352160768000000,265252859812191058636308480000000,
%U 263130836933693530167218012160000000
%N Factorials F which have at least one prime neighbor, i.e., F+1 or F1 or both are primes.
%C Conjecture: sequence is infinite. But there are finitely many members which are sandwiched between twin primes.
%H Robert Israel, <a href="/A088258/b088258.txt">Table of n, a(n) for n = 1..28</a>
%F a(n) = A088412(n)! = A000142(A088412(n)).  _Robert Israel_, Aug 25 2016
%e 2 is in the sequence because 2 + 1 is prime.
%e 6 is in the sequence because both 6  1 and 6 + 1 are prime.
%e 24 is in the sequence because 24  1 is prime.
%p select(t > isprime(t+1) or isprime(t1), [seq(n!,n=1..100)]); # _Robert Israel_, Aug 25 2016
%t Select[Range[32]!, Or @@ PrimeQ@ {#  1, # + 1} &] (* _Michael De Vlieger_, Aug 25 2016 *)
%Y Cf. A000142, A088256, A088257, A088412.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Sep 27 2003
%E More terms from _Ray Chandler_, Sep 28 2003
