GCD of the numbers binomial(2*prime(n), 2*k) for k = 1..prime(n)-1.
6, 15, 15, 91, 11, 65, 17, 703, 23, 29, 1891, 2701, 123, 43, 47, 53, 59, 671, 67, 71, 73, 12403, 83, 89, 18721, 101, 103, 107, 109, 113, 127, 131, 137, 38503, 149, 151, 49141, 163, 167, 173, 179, 3439, 191, 193, 197, 79003, 88831, 223, 227, 104653, 233
1
The highest points in the graph are at primes p such that 2*p-1 is also prime, which is A005382. The absissa at those p is p*(2*p-1) The lowest points are at the primes given in S000740.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Carl McTague, On the greatest common divisor of binomial(qn,q), binomial(qn,2q),..., binomial(qn,qn-q), arXix 1510.06696 (Oct 22 2015).
(Mma) Table[GCD @@ Table[Binomial[2*n, 2*k], {k, n - 1}], {n, Prime[Range[100]]}]
nonn
T. D. Noe, Oct 27 2015