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%I #8 Nov 02 2024 03:21:41
%S 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,
%T 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,
%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N Conjectured least prime p for which binomial(n*q,q) (mod q^3) = n for all primes q >= p.
%C The n = 2 case is mentioned in Eric Weisstein's website.
%H T. D. Noe, <a href="/A222760/b222760.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">MathWorld: Central Binomial Coefficient</a>
%t 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}]
%Y Cf. A096328 (prime(prime(n)^3)), A222759.
%K nonn
%O 1,1
%A _T. D. Noe_, Mar 13 2013