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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. 3

%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 F-1 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(t-1), [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

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Last modified September 17 04:49 EDT 2019. Contains 327119 sequences. (Running on oeis4.)