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

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000108(n^2) mod A000040(n).

Mathematica

Table[Mod[CatalanNumber[n^2], Prime[n]], {n, 80}]

Prog

(Magma) [Catalan(n^2) mod NthPrime(n): n in [1..100]];
(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

Crossrefs

Cf. A000040, A214441, A246714, A254706.

Sequence in context: A074476 A224610 A265819 * A011021 A077232 A193891

Adjacent sequences: A254743 A254744 A254745 * A254747 A254748 A254749

Keyword

nonn

Author

Vincenzo Librandi, Feb 07 2015

Status

approved