A053427 Numbers n such that Catalan(n)-1 is prime.

4, 5, 6, 8, 9, 18, 25, 66, 87, 134, 145, 200, 384, 443, 502, 589, 625, 638, 1082, 1235, 1236, 1439, 1892, 2014, 2355, 2380, 2592, 2676, 2981, 3406, 3908, 4775, 5885, 10617, 16108, 17035, 18164, 18307, 20565, 24542, 26388, 32786, 47379, 49711, 50103, 55067

Offset: 1

Author

David Broadhurst, Jan 10 2000

Keywords

• nonn

Comments

Primality up to Catalan(5885)-1 proved by PrimeForm.

The next term, if it exists, is > 60000. - Vaclav Kotesovec, Apr 26 2021

Examples

			Catalan(25)-1 = 50!/25!/26!-1 = 4861946401451 is prime.
		

Crossrefs

Cf. A000108, A053429.

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 *)

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 5886 to 100000
Charles R Greathouse IV, Jan 03 2014

Extensions

a(34)-a(41) from Charles R Greathouse IV, Jan 03 2014

a(42) from Vaclav Kotesovec, Apr 20 2021

a(43)-a(46) from Vaclav Kotesovec, Apr 25 2021