OFFSET
1,1
COMMENTS
Next term a(7) has 475 decimal digits and is too large to include. Corresponding numbers k such that the sum of first k Catalan numbers is a prime are listed in A134775.
LINKS
Eric Weisstein's World of Mathematics, Catalan Number
EXAMPLE
a(1) = 3 because C(1) + C(2) = 1 + 2 = 3 is a prime.
a(2) = 6917 because C(1) + C(2) + C(3) + C(4) + C(5) + C(6) + C(7) + C(8) + C(9) = 1 + 2 + 5 + 14 + 42 + 132 + 429 + 1430 + 4862 = 6917 is a prime.
MATHEMATICA
f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} ] ], {n, 1, 1000} ]
Select[Accumulate[CatalanNumber[Range[200]]], PrimeQ] (* Harvey P. Dale, Mar 01 2019 *)
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Alexander Adamchuk, Nov 11 2007
STATUS
approved