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

Author

Vincenzo Librandi, Sep 02 2014

Keywords

• nonn

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

Crossrefs

Cf. A000040, A000108.

Programs

Magma

[Catalan(n) mod NthPrime(n): n in [1..70]];

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 *)

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