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Primes of the form (2n)! - n! + 1.
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%I #21 May 05 2018 13:02:47

%S 2,23,87178286161,403291461126605629356979201,

%T 5502622159812088949850305428800254867109635014075023360001

%N Primes of the form (2n)! - n! + 1.

%C The next term, if it exists, has more than 7500 digits. - _M. F. Hasler_, Feb 09 2014

%C Primes in sequence A237580 = n -> (2n)! - n! + 1, i.e., the terms of that sequence which coincide with A237579(n) = least prime factor of (2n)! - n! + 1. - _M. F. Hasler_, Feb 09 2014

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

%F A118812 = A237580 o A237443 = A237579 o A237443. - _M. F. Hasler_, Feb 09 2014

%e For n=2, (2*2)! - 2! + 1 = 24 - 2 + 1 = 23, which is prime.

%p PFACT:=proc(N) local i,r; for i from 1 by 1 to N do r:=(2*i)!-i!+1; if isprime(r) then print(i); fi; od; end: PFACT(100);

%t Select[Table[(2n)!-n!+1,{n,30}],PrimeQ] (* _Harvey P. Dale_, May 05 2018 *)

%o (PARI) for(n=1,999,ispseudoprime(p=(2*n)!-n!+1)&&print1(p",")) \\ _M. F. Hasler_, Feb 09 2014

%Y Cf. A237443 (corresponding values of n).

%K nonn

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 23 2006