A075840 - OEIS

%I #20 Sep 08 2022 08:45:07

%S 2,3,7,71,3433,2704157,35345263801,2104098963721,

%T 6892620648693261354601,410795449442059149332177041,

%U 1520803477811874490019821888415218657,5949105755928259715106809205795376486501,1480212998448786189993816895482588794876101

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

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

%H Charles R Greathouse IV, <a href="/A075840/b075840.txt">Table of n, a(n) for n = 1..25</a>

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

%t a = Select[ Range[100], PrimeQ[Binomial[2#, # ] + 1] & ]; Binomial[2a, a] + 1

%t Select[Table[(2 n)! / (n!)^2 + 1, {n, 0, 80}], PrimeQ] (* _Vincenzo Librandi_, Mar 17 2015 *)

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

%o (Magma) [a: n in [0..100] | IsPrime(a) where a is Factorial(2*n) div Factorial(n)^2+1]; // _Vincenzo Librandi_ Mar 17 2015

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

%Y Cf. A000984, n's are in A066699.

%K nonn

%O 1,1

%A _Donald S. McDonald_, Oct 14 2002

%E Edited by _Robert G. Wilson v_, Oct 15 2002

%E Definition corrected by _Alexander Adamchuk_, Nov 30 2007

%E Edited by _N. J. A. Sloane_, Nov 30 2007

%E a(13) from _Vincenzo Librandi_, Mar 17 2015