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A246714
Catalan(n) mod prime(n).
5
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
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
Sequence in context: A346255 A346480 A323399 * A246708 A249387 A350487
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Sep 02 2014
STATUS
approved