A119662 Primes of the form k! + k^2 + 1.

2, 3, 7, 41, 757

Offset: 1

Author

Jonathan Vos Post, Jul 28 2006

Keywords

• nonn

Comments

Primes of the form A004664(k) + 1.

For k! + k^2 + 1 to be prime, k > 1, it is necessary but not sufficient for k to be even.

No more terms for k < 1150. [Vincenzo Librandi, Dec 22 2010]

Crossrefs

Cf. A000040, A004664, A119448.

Programs

Magma

[ a: n in [0..1150] | IsPrime(a) where a is Factorial(n)+n^2+1 ]; // Vincenzo Librandi, Dec 22 2010

Mathematica

lst={}; Do[s=n!+n^2;If[PrimeQ[p=s+1], AppendTo[lst, p]], {n, 0, 5!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)

Formula

A000040 INTERSECTION A227546 = primes INTERSECTION {k! + k^2 + 1}.