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A246714 Catalan(n) mod prime(n).

%I A246714 #21 May 22 2025 10:21:40
%S A246714 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 A246714 101,4,20,8,16,18,53,127,25,139,4,54,149,127,176,156,71,17,65,196,10,
%U A246714 211,221,205,63,138,137,234,254,194,67,243,155,145,164,203,76,187,272
%N A246714 Catalan(n) mod prime(n).
%C A246714 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 A246714 a(n) = 1 for n = 1, 1161, 15792. - _Jens Kruse Andersen_, Sep 02 2014
%H A246714 Jens Kruse Andersen, <a href="/A246714/b246714.txt">Table of n, a(n) for n = 1..10000</a>
%p A246714 seq(binomial(2*n,n)/(n+1) mod ithprime(n), n=1..100); # _Robert Israel_, Sep 02 2014
%t A246714 Table[Mod[CatalanNumber[n], Prime[n]], {n, 65}] (* _Alonso del Arte_, Sep 02 2014 *)
%o A246714 (Magma) [Catalan(n) mod NthPrime(n): n in [1..70]];
%o A246714 (Python)
%o A246714 from sympy import prime
%o A246714 from gmpy2 import divexact, t_mod
%o A246714 A246714, c = [1], 1
%o A246714 for n in range(2,10**3):
%o A246714     c = divexact(c*(4*n-2),(n+1))
%o A246714     A246714.append(t_mod(c,prime(n))) # _Chai Wah Wu_, Sep 04 2014
%Y A246714 Cf. A000040, A000108.
%K A246714 nonn
%O A246714 1,2
%A A246714 _Vincenzo Librandi_, Sep 02 2014