Prime numbers that are the sum of consecutive 13-gonal numbers.
13, 409, 643, 1609, 2251, 4019, 4441, 5711, 7489, 8429, 8681, 10891, 11329, 12569, 13411, 17681, 19489, 19751, 23369, 37379, 42239, 42409, 48049, 51001, 58601, 63689, 75389, 82891, 85361, 91811, 96643, 101921, 112559, 114649, 115301, 128521, 133321
1
The only prime 13-gonal number is 13, the first term. Other terms are the sum of 2, 3, or 6 consecutive 13-gonal numbers.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Polygonal number
(Mma) nn = 400; f = 13; s = Table[k ((f - 2) k - (f - 4))/2, {k, nn}]; t = Table[Select[Plus @@@ Partition[s, n, 1], PrimeQ], {n, 6}]; mx = Min[Select[Max /@ Rest[t], # > 0 &]]; Select[Union[Flatten[t]], # <= mx &]
Cf. A163251 (squares), S000790-S000798.
nonn
T. D. Noe, Dec 11 2015