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Primes of the form n! - n!! + 1.
1

%I #8 Dec 17 2018 19:45:28

%S 17,673,39937,87177646081,6402373519933441,

%T 304888344611712432172380979201,

%U 126886932185884164103433389335161480802865515044406852999479261820223930701069680640000001

%N Primes of the form n! - n!! + 1.

%C The next term -- a(8) -- has 675 digits. - _Harvey P. Dale_, Dec 17 2018

%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 159.

%e For n=4, 4! - 4!! + 1 = 4*3*2*1 - 4*2 + 1 = 24 - 8 + 1 = 17, which is prime.

%p SFACT:= proc(n) local i,j,k; for k from 1 by 1 to n do i:=k; j:=k-2; while j >0 do i:=i*j; j:=j-2; od: if isprime(k!-i+1) then print(k!-i+1); fi; od: end: SFACT(300);

%t Select[Table[n!-n!!+1,{n,70}],PrimeQ] (* _Harvey P. Dale_, Dec 17 2018 *)

%K nonn

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 22 2006