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

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

Offset

1,1

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

Example

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

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 *)

Prog

(PARI) v=[]; for(n=0, 100, x=bin(2*n, n)+1; if(isprime(x), v=concat(v, x), )); v
(Magma) [a: n in [0..100] | IsPrime(a) where a is Factorial(2*n) div Factorial(n)^2+1]; // Vincenzo Librandi Mar 17 2015

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.

Sequence in context: A130309 A090870 A088542 * A096225 A333132 A035094

Adjacent sequences: A075837 A075838 A075839 * A075841 A075842 A075843

Keyword

nonn

Author

Donald S. McDonald, Oct 14 2002

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

Status

approved