A246714 Catalan(n) mod prime(n).

1, 2, 0, 0, 9, 2, 4, 5, 9, 5, 10, 35, 21, 12, 14, 45, 19, 38, 36, 20, 54, 54, 19, 10, 83, 40, 101, 4, 20, 8, 16, 18, 53, 127, 25, 139, 4, 54, 149, 127, 176, 156, 71, 17, 65, 196, 10, 211, 221, 205, 63, 138, 137, 234, 254, 194, 67, 243, 155, 145, 164, 203, 76, 187, 272

Offset

1,2

Comments

Since prime(n) > 2*n for n > 4, the only occurrences of 0 are at n = 3 and 4. Are there any occurrences of 1 after n = 1? - Robert Israel, Sep 02 2014

a(n) = 1 for n = 1, 1161, 15792. - Jens Kruse Andersen, Sep 02 2014

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Maple

seq(binomial(2*n, n)/(n+1) mod ithprime(n), n=1..100); # Robert Israel, Sep 02 2014

Mathematica

Table[Mod[CatalanNumber[n], Prime[n]], {n, 65}] (* Alonso del Arte, Sep 02 2014 *)

Prog

(Magma) [Catalan(n) mod NthPrime(n): n in [1..70]];
(Python)
from sympy import prime
from gmpy2 import divexact, t_mod
A246714, c = [1], 1
for n in range(2, 10**3):
....c = divexact(c*(4*n-2), (n+1))
....A246714.append(t_mod(c, prime(n))) # Chai Wah Wu, Sep 04 2014

Crossrefs

Cf. A000040, A000108.

Sequence in context: A346255 A346480 A323399 * A246708 A249387 A350487

Adjacent sequences: A246711 A246712 A246713 * A246715 A246716 A246717

Keyword

nonn

Author

Vincenzo Librandi, Sep 02 2014

Status

approved