GCD of the numbers binomial(3*prime(n), 3*k) for k = 1..prime(n)-1.
20, 84, 455, 266, 1364, 9139, 595, 133, 3082, 1247, 31, 4033, 27511, 21844, 6533, 657359, 59, 143533, 13333, 14981, 7957, 79, 83, 89, 1649, 15251, 31621, 214, 17767, 495053, 914527, 917, 56033, 139, 33227, 151, 157, 79381, 83333, 173, 179, 26536591
1
The highest points in the graph are at those primes p such that (3/2)(p-1)+1 and 3p-2 are also prime. Those primes appear in S000741.
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[3*n, 3*k], {k, n - 1}], {n, Prime[Range[100]]}]
nonn
T. D. Noe, Oct 27 2015