A222760 Conjectured least prime p for which binomial(n*q,q) (mod q^3) = n for all primes q >= p.

2, 5, 3, 2, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

T. D. Noe, Mar 13 2013

Keywords

• nonn

Comments

The n = 2 case is mentioned in Eric Weisstein's website.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Eric W. Weisstein, MathWorld: Central Binomial Coefficient

Crossrefs

Cf. A096328 (prime(prime(n)^3)), A222759.

Programs

Mathematica

lim = 100; Table[r = Table[Mod[Binomial[n*p, p], p^3] == n, {p, Prime[Range[lim]]}]; i = lim; While[i > 0 && r[[i]], i--]; Prime[i + 1], {n, 87}]