A364694 Polygonal numbers of order greater than 2 (A090466) which are the sum of the first k primes, for some k > 0.

10, 28, 58, 100, 129, 160, 238, 328, 381, 501, 568, 639, 712, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 2127, 2276, 2427, 2584, 2914, 3087, 3447, 3831, 4227, 4438, 4888, 5350, 5589, 5830, 6081, 6601, 6870, 8275, 10191, 10887, 11599, 12339, 12718

Offset: 1

Author

Paolo Xausa, Aug 03 2023

Keywords

• nonn

Examples

			28 is a term because it's both a triangular number and the sum of the first 5 primes (2 + 3 + 5 + 7 + 11).
58 is a term because it's both an octagonal number and the sum of the first 7 primes (2 + 3 + 5 + 7 + 11 + 13 + 17).
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Polygonal number.
• Index to sequences related to polygonal numbers

Crossrefs

Intersection of A007504 with A090466.

Cf. A061890, A066527, A364691, A364695.

Programs

Mathematica

A364693Q[n_]:=With[{d=Divisors[2n]},Catch[For[i=3,iJianing Song in A090466 *)
A364694list[kmax_]:=Select[Accumulate[Prime[Range[kmax]]],A364693Q];A364694list[100]