A364696 Nonnegative integers k such that the sum of the first k primes is a pentagonal number.

0, 2, 77, 24587, 48070640, 471412484, 7471587112

Offset: 1

Author

Paolo Xausa, Aug 03 2023

Keywords

• nonn
• hard
• more

Examples

			2 is a term because the sum of the first 2 primes (2 + 3 = 5) is a pentagonal number.
		

Links

• Wikipedia, Pentagonal number.
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000326, A007504, A033997, A175133, A364691, A364695, A366270.

Programs

Mathematica

A364696list[kmax_]:=Module[{p=0},Join[{0},Table[If[IntegerQ[(Sqrt[24(p+=Prime[k])+1]+1)/6],k,Nothing],{k,kmax}]]];A364696list[25000] (* Paolo Xausa, Oct 06 2023 *)

Extensions

a(5) from Michel Marcus, Aug 04 2023

a(6)-a(7) from Hugo Pfoertner, Aug 04 2023