Primes p such that p = GCD of the numbers binomial(2*p, 2*k) for k = 1..p-1.
11, 17, 23, 29, 43, 47, 53, 59, 67, 71, 73, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 149, 151, 163, 167, 173, 179, 191, 193, 197, 223, 227, 233, 239, 241, 251, 257, 263, 269, 277, 281, 283, 293, 311, 317, 347, 349, 353, 359, 373, 383, 389, 397, 401
1
Primes not in this sequence are the union of A005382 and a sparse set of primes.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) nn = 100; Select[Prime[Range[2*nn]], # == GCD @@ Table[Binomial[2*#, 2*k], {k, # - 1}] &, nn]
nonn
T. D. Noe, Oct 27 2015