A134775 Numbers k such that the sum of first k Catalan numbers is a prime.

2, 9, 11, 31, 46, 146, 795, 2773, 2788, 9797

Offset

1,1

Comments

Corresponding primes are listed in A134776. A134776(n) = A014138(a(n)-1).

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Catalan Number

Example

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.

Maple

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, Nov 19 2007

Mathematica

f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} ] ], {n, 1, 1000} ]
Flatten[Position[Accumulate[CatalanNumber[Range[1000]]], _?PrimeQ]] (* Harvey P. Dale, Jan 28 2013 *)

Crossrefs

Cf. A134776 (primes that are the sum of first n Catalan numbers).

Cf. A014138 (partial sums of Catalan numbers).

Cf. A000108 (Catalan numbers).

Sequence in context: A065596 A280418 A042053 * A042573 A041651 A042687

Adjacent sequences: A134772 A134773 A134774 * A134776 A134777 A134778

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Nov 11 2007

Extensions

2 more terms from Emeric Deutsch, Nov 19 2007

9797 from Ryan Propper, Jan 06 2008

Status

approved