A162455 Primes of the form (n!)^2 + (n!) + 1.

3, 7, 43, 601, 519121

Offset: 1

Author

Daniel Tisdale, Jul 03 2009

Keywords

• nonn

Comments

a(6) is associated with 76!=A000142(76)=A051856(7)! and has 223 decimal digits. - R. J. Mathar, Emeric Deutsch and Harvey P. Dale, Jul 14 2009

a(6) =

355509027001074785420251313577077264819432566692554164797700525028005\

008417722668844213916658906516439209129303887999464691915088148300993\

913093163021697465163231343499013584682565554967153792311772997222400\

0000000000000001. - N. J. A. Sloane, Jul 11 2010

Programs

Maple

a := proc (n) if isprime(factorial(n)^2+factorial(n)+1) = true then factorial(n)^2+factorial(n)+1 else end if end proc: seq(a(n), n = 1 .. 76); # Emeric Deutsch, Jul 21 2009

Mathematica

Select[Table[n!^2+n!+1,{n,150}],PrimeQ] (* Harvey P. Dale, Jul 23 2009 *)
Select[#^2+#+1&/@(Range[150]!),PrimeQ] (* Harvey P. Dale, Nov 24 2024 *)

Formula

a(n) = A002061(A000142(A051856(n+1))+1). - R. J. Mathar, Jul 14 2009