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A254746 a(n) = Catalan(n^2) mod prime(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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, A000108, 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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)