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

0, 1, 2, 5, 11, 25, 69, 86, 90, 95, 104, 145, 203, 215, 227, 291, 309, 322, 337, 407, 480, 792, 823, 919, 1001, 1159, 2226, 2743, 2822, 4250, 8077, 8109, 16024, 17422, 23941, 25212, 25379, 28753, 30510, 31748, 33613, 45622

Offset: 1

Author

David Broadhurst, Jan 10 2000

Keywords

• nonn

Comments

Primality up to Catalan(4250)+1 proved by PrimeForm.

The next term, if it exists, is > 50000. - Vaclav Kotesovec, Apr 27 2021

Examples

			Catalan(25)+1 = 50!/25!/26!+1 = 4861946401453 is prime.
		

Crossrefs

Cf. A000108, A053427.

Programs

Mathematica

Reap[ Do[ If[ PrimeQ[ CatalanNumber[n] + 1], Print[n]; Sow[n]], {n, 0, 10^4}]][[2, 1]] (* Jean-François Alcover, Feb 02 2015 *)
Select[Range[0,29000],PrimeQ[CatalanNumber[#]+1]&] (* Harvey P. Dale, Apr 14 2019 *)

PARI

is(n)=ispseudoprime(binomial(2*n, n)/(n+1)-1) \\ Charles R Greathouse IV, Jan 03 2014

PFGW

ABC2 C(2*$a, $a)/($a+1)+1
a: from 0 to 100000
Charles R Greathouse IV, Jan 03 2014

Extensions

a(31)-a(38) from Charles R Greathouse IV, Jan 04 2014

a(39)-a(41) from Vaclav Kotesovec, Apr 20 2021

a(42) from Vaclav Kotesovec, Apr 26 2021