A075840 Primes of the form (2*n)!/(n!)^2+1.

2, 3, 7, 71, 3433, 2704157, 35345263801, 2104098963721, 6892620648693261354601, 410795449442059149332177041, 1520803477811874490019821888415218657, 5949105755928259715106809205795376486501, 1480212998448786189993816895482588794876101

Offset: 1

Author

Donald S. McDonald, Oct 14 2002

Keywords

• nonn

Examples

			7 is a term because C(4,2)+1 = 6+1 = 7 is prime.
		

References

• New Zealand Science Monthly, Bulletin Board, Feb. 1999. Binomial(300,150)+185 = nextprime.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A092751 = n such that (2*n)!/(n!)^2+1 is prime, A112858 = primes of the form (2*n)!/(n!)^2-1.

Cf. A000984, n's are in A066699.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is Factorial(2*n) div Factorial(n)^2+1]; // Vincenzo Librandi Mar 17 2015

Mathematica

a = Select[ Range[100], PrimeQ[Binomial[2#, # ] + 1] & ]; Binomial[2a, a] + 1
Select[Table[(2 n)! / (n!)^2 + 1, {n, 0, 80}], PrimeQ] (* Vincenzo Librandi, Mar 17 2015 *)

PARI

v=[]; for(n=0,100,x=bin(2*n,n)+1; if(isprime(x), v=concat(v,x),)); v

Extensions

Edited by Robert G. Wilson v, Oct 15 2002

Definition corrected by Alexander Adamchuk, Nov 30 2007

Edited by N. J. A. Sloane, Nov 30 2007

a(13) from Vincenzo Librandi, Mar 17 2015