%I #20 Apr 26 2021 11:33:53

%S 4,5,6,8,9,18,25,66,87,134,145,200,384,443,502,589,625,638,1082,1235,

%T 1236,1439,1892,2014,2355,2380,2592,2676,2981,3406,3908,4775,5885,

%U 10617,16108,17035,18164,18307,20565,24542,26388,32786,47379,49711,50103,55067

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

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

%C The next term, if it exists, is > 60000. - _Vaclav Kotesovec_, Apr 26 2021

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

%t Reap[ Do[ If[ PrimeQ[ CatalanNumber[n] - 1], Print[n]; Sow[n]], {n, 0, 10^4}]][[2, 1]] (* _Jean-François Alcover_, Feb 02 2015 *)

%o (PARI) is(n)=ispseudoprime(binomial(2*n,n)/(n+1)-1) \\ _Charles R Greathouse IV_, Jan 03 2014

%o (PFGW) ABC2 C(2*$a,$a)/($a+1)-1

%o a: from 5886 to 100000

%o _Charles R Greathouse IV_, Jan 03 2014

%Y Cf. A000108, A053429.

%K nonn

%O 1,1

%A _David Broadhurst_, Jan 10 2000

%E a(34)-a(41) from _Charles R Greathouse IV_, Jan 03 2014

%E a(42) from _Vaclav Kotesovec_, Apr 20 2021

%E a(43)-a(46) from _Vaclav Kotesovec_, Apr 25 2021