A254746 a(n) = Catalan(n^2) mod prime(n).
1, 2, 2, 5, 8, 0, 0, 11, 0, 24, 0, 0, 29, 0, 0, 0, 0, 39, 58, 0, 21, 33, 9, 69, 9, 0, 16, 86, 0, 0, 0, 0, 0, 64, 139, 0, 0, 0, 75, 12, 4, 0, 0, 119, 195, 0, 193, 202, 0, 0, 55, 218, 0, 0, 0, 0, 84, 201, 0, 0, 203, 275, 0, 198, 159, 0, 0, 0, 0, 255, 13, 204, 0
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
-
Magma
[Catalan(n^2) mod NthPrime(n): n in [1..100]];
-
Mathematica
Table[Mod[CatalanNumber[n^2], Prime[n]], {n, 80}] -
Python
from sympy import factorint, prime A254746_list, c, s, s2 = [1], {}, 2, 4 for n in range(2,10**3+1): for p,e in factorint(4*n-2).items(): if p in c: c[p] += e else: c[p] = e for p,e in factorint(n+1).items(): if c[p] == e: del c[p] else: c[p] -= e if n == s2: d, ps = 1, prime(s) for p,e in c.items(): d = (d*pow(p,e,ps)) % ps A254746_list.append(d) s2 += 2*s+1 s += 1 # Chai Wah Wu, Feb 14 2015