A246714 - OEIS

%I #19 Sep 08 2022 08:46:09

%S 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,

%T 101,4,20,8,16,18,53,127,25,139,4,54,149,127,176,156,71,17,65,196,10,

%U 211,221,205,63,138,137,234,254,194,67,243,155,145,164,203,76,187,272

%N Catalan(n) mod prime(n).

%C 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

%C a(n) = 1 for n = 1, 1161, 15792. - _Jens Kruse Andersen_, Sep 02 2014

%H Jens Kruse Andersen, <a href="/A246714/b246714.txt">Table of n, a(n) for n = 1..10000</a>

%p seq(binomial(2*n,n)/(n+1) mod ithprime(n), n=1..100); # _Robert Israel_, Sep 02 2014

%t Table[Mod[CatalanNumber[n], Prime[n]], {n, 65}] (* _Alonso del Arte_, Sep 02 2014 *)

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

%o (Python)

%o from sympy import prime

%o from gmpy2 import divexact, t_mod

%o A246714, c = [1], 1

%o for n in range(2,10**3):

%o ....c = divexact(c*(4*n-2),(n+1))

%o ....A246714.append(t_mod(c,prime(n))) # _Chai Wah Wu_, Sep 04 2014

%Y Cf. A000040, A000108.

%K nonn

%O 1,2

%A _Vincenzo Librandi_, Sep 02 2014