A222759 -id:A222759 - cp's OEIS frontend

A096328 Prime(p^3) where p = prime(n).

19, 103, 691, 2309, 10957, 19403, 47657, 69031, 130073, 279431, 347707, 620531, 867677, 1013609, 1353887, 1999121, 2829503, 3152099, 4268039, 5145347, 5628457, 7258871, 8510507, 10651117, 14042671, 15986303, 17023271, 19235537, 20411623, 22909613, 33289481

Offset: 1

Cino Hilliard, Aug 02 2004

nonn

			5 = prime(3). Hence, a(3) = prime(5^3) = prime(125) = 691.
7 = prime(4). Hence, a(4) = prime(7^3) = prime(343) = 2309.

T. D. Noe, Table of n, a(n) for n = 1..100

Cf. A222759.

Table[ Prime[ Prime[n]^3], {n, 29}] (* Robert G. Wilson v, Aug 07 2004 *)

g(n,m) = forprime(j=2,m, forprime(x=2,n,print1(prime(j^3)",");break))

Edited by Robert G. Wilson v, Aug 07 2004

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

Original entry on oeis.org

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

T. D. Noe, Mar 13 2013

nonn

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

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

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

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}]

cp's OEIS Frontend

A096328 Prime(p^3) where p = prime(n).

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