A046029 Numbers k such that (k!)^2 + 1 is prime.
0, 1, 2, 3, 4, 5, 9, 10, 11, 13, 24, 65, 76, 127162
Offset: 1
Examples
9 is a term because (9!)^2 + 1 is prime.
References
- H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
Links
- Mike 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
Programs
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Magma
[n: n in [0..90] |IsPrime(Factorial(n)^2+1)]; // Vincenzo Librandi, May 28 2015
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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 *)
Extensions
a(14) from Ryan Propper, Jun 25 2025
Comments