A230061 Primes of the form Catalan(n)+1.

2, 3, 43, 58787, 4861946401453, 337485502510215975556783793455058624701, 4180080073556524734514695828170907458428751314321, 1000134600800354781929399250536541864362461089950801, 944973797977428207852605870454939596837230758234904051

Offset: 1

Author

K. D. Bajpai, Oct 08 2013

Keywords

• nonn

Comments

The 25th term a(25) in the sequence has 693 digits.

a(26) has 1335 digits; a(27) has 1647 digits; a(28) has 1694 digits; a(29) has 2554 digits; a(30) has 4857 digits; a(31) has 4876 digits; a(32) has 9641 digits. - Charles R Greathouse IV, Oct 09 2013

Examples

			a(3)= 43: Catalan(5)= (2*5)!/(5!*(5+1)!)= 42. Catalan(5)+1= 43 which is prime.
a(4)= 58787: Catalan(11)= (2*11)!/(11!*(11+1)!)= 58786. Catalan(11)+1= 58787 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..25
• Chris K. Caldwell and G. L. Honaker,Jr., Prime Curios! 4250

Crossrefs

Cf. A000108, A024492, A141351.

Cf. A053429 (numbers n such that Catalan(n)+1 is prime).

Programs

Maple

KD:= proc() local a,b,c; a:= (2*n)!/(n!*(n + 1)!); b:=a+1;if isprime(b) then return(b): fi; end: seq(KD(),n=1..50);

Mathematica

Select[CatalanNumber[Range[100]]+1,PrimeQ] (* Harvey P. Dale, Aug 26 2021 *)

PARI

for(n=1,1e3,if(ispseudoprime(t=binomial(2*n,n)/(n+1)+1),print1(t", "))) \\ Charles R Greathouse IV, Oct 08 2013