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A088258 Factorials F which have at least one prime neighbor, i.e., F+1 or F-1 or both are primes.

%I A088258 #19 Jul 29 2017 13:16:42
%S A088258 1,2,6,24,720,5040,39916800,479001600,87178291200,
%T A088258 10888869450418352160768000000,265252859812191058636308480000000,
%U A088258 263130836933693530167218012160000000
%N A088258 Factorials F which have at least one prime neighbor, i.e., F+1 or F-1 or both are primes.
%C A088258 Conjecture: sequence is infinite. But there are finitely many members which are sandwiched between twin primes.
%H A088258 Robert Israel, <a href="/A088258/b088258.txt">Table of n, a(n) for n = 1..28</a>
%F A088258 a(n) = A088412(n)! = A000142(A088412(n)). - _Robert Israel_, Aug 25 2016
%e A088258 2 is in the sequence because 2 + 1 is prime.
%e A088258 6 is in the sequence because both 6 - 1 and 6 + 1 are prime.
%e A088258 24 is in the sequence because 24 - 1 is prime.
%p A088258 select(t -> isprime(t+1) or isprime(t-1), [seq(n!,n=1..100)]); # _Robert Israel_, Aug 25 2016
%t A088258 Select[Range[32]!, Or @@ PrimeQ@ {# - 1, # + 1} &] (* _Michael De Vlieger_, Aug 25 2016 *)
%Y A088258 Cf. A000142, A088256, A088257, A088412.
%K A088258 nonn
%O A088258 1,2
%A A088258 _Amarnath Murthy_, Sep 27 2003
%E A088258 More terms from _Ray Chandler_, Sep 28 2003