Figurate primes, numbers of the form binomial(p^x,y), where p is prime and x and y are positive integers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 23, 25, 27, 28, 29, 31, 32, 35, 36, 37, 41, 43, 47, 49, 53, 55, 56, 59, 61, 64, 67, 70, 71, 73, 78, 79, 81, 83, 84, 89, 97, 101, 103, 107, 109, 113, 120, 121, 125, 126, 127, 128, 131, 136, 137, 139, 149

1

Defined by Cai.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Tianxin Cai, The Book of Numbers, High Education Press, Beijing, 2014.

Tianxin Cai, Yong Zhang, and Zhongyan Shen, Figurate primes and Hilbert's 8th problem, arXiv 1406.5661, Jun 22 2014.

(Mma) lim = 100; Select[Union[Flatten[Table[Binomial[p^a, i], {i, lim}, {p, Prime[Range[lim]]}, {a, Log[lim]}]]], # < Prime[lim] &]

nonn

T. D. Noe, Jun 23 2014