1,1

Corresponding primes are listed in A134776(n) = {3, 6917, 82499, 19720133460129649, 11784299926611415613401489, ...} = A014138(a(n)-1).

Eric Weisstein, Link to a section of The World of Mathematics. Catalan Number.

a(1) = 2 because C(1) + C(2) = 1 + 2 = 3 is a prime.

a(2) = 9 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.

for n to 3000 do c[n]:= binomial(2*n, n)/(n+1) end do: a:=proc(n) if isprime(add(c[j], j=1..n))=true then n else end if end proc: seq(a(n), n=1..3000); -Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 19 2007

f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} ] ], {n, 1, 1000} ]

Cf. A134776 = Primes that are the sum of first n Catalan numbers. Cf. A014138 = Partial sums of Catalan numbers (starting 1, 2, 5, ..., cf. A000108). Cf. A000108 = Catalan numbers.

Sequence in context: A115911 A065596 A042053 this_sequence A042573 A041651 A042687

Adjacent sequences: A134772 A134773 A134774 this_sequence A134776 A134777 A134778

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 11 2007

2 more terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 19 2007

9797 from Ryan Propper (rpropper(AT)cs.stanford.edu), Jan 06 2008