A046029 Numbers k such that (k!)^2 + 1 is prime.

0, 1, 2, 3, 4, 5, 9, 10, 11, 13, 24, 65, 76

Offset

1,3

Comments

a(14) > 780. - Ralf Stephan, Oct 21 2002

a(14) > 2500. - Gabriel Cunningham (gcasey(AT)mit.edu), Feb 23 2004

a(14) > 10000. - Charles R Greathouse IV, Nov 16 2006

a(14) > 16000. - Robert Price, Aug 13 2011

References

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

Links

Table of n, a(n) for n=1..13.

M. Oakes, Re: Gaussian primorial and factorial primes, Primeform, Dec 21 2010

Mike Oakes, Andrew Walker, David Broadhurst, Gaussian primorial and factorial primes, digest of 7 messages in primeform Yahoo group, Dec 20 - Dec 21, 2010.

Eric Weisstein's World of Mathematics, Factorial

Example

9 is a term because (9!)^2 + 1 is prime.

Mathematica

Do[ If[ PrimeQ[n!^2 + 1], Print[n]], {n, 500}] (* Robert G. Wilson v, Apr 14 2004 *)
Select[Range[1000], PrimeQ[(#!^2 + 1)] &] (* Vincenzo Librandi, May 28 2015 *)

Prog

(Magma) [n: n in [0..90] |IsPrime(Factorial(n)^2+1)]; // Vincenzo Librandi, May 28 2015

Crossrefs

Cf. A020549, A051739.

Sequence in context: A328119 A118732 A118872 * A303600 A194410 A361125

Adjacent sequences: A046026 A046027 A046028 * A046030 A046031 A046032

Keyword

nonn,more,hard

Author

Eric W. Weisstein

Status

approved