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

1, 2, 6, 24, 720, 5040, 39916800, 479001600, 87178291200, 10888869450418352160768000000, 265252859812191058636308480000000, 263130836933693530167218012160000000

Offset: 1

Author

Amarnath Murthy, Sep 27 2003

Keywords

• nonn

Comments

Conjecture: sequence is infinite. But there are finitely many members which are sandwiched between twin primes.

Examples

			2 is in the sequence because 2 + 1 is prime.
6 is in the sequence because both 6 - 1 and 6 + 1 are prime.
24 is in the sequence because 24 - 1 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..28

Crossrefs

Cf. A000142, A088256, A088257, A088412.

Programs

Maple

select(t -> isprime(t+1) or isprime(t-1), [seq(n!,n=1..100)]); # Robert Israel, Aug 25 2016

Mathematica

Select[Range[32]!, Or @@ PrimeQ@ {# - 1, # + 1} &] (* Michael De Vlieger, Aug 25 2016 *)

Formula

a(n) = A088412(n)! = A000142(A088412(n)). - Robert Israel, Aug 25 2016

Extensions

More terms from Ray Chandler, Sep 28 2003