A366269 Hexagonal numbers which are the sum of the first k primes, for some k >= 0.

0, 28, 54047322253, 14756071005948636, 600605016143706003, 41181981873797476176, 240580227206205322973571

Offset: 1

Author

Paolo Xausa, Oct 06 2023

Keywords

• nonn
• hard
• more

Examples

			28 is a term because it's both a hexagonal number and the sum of the first five primes (2 + 3 + 5 + 7 + 11).
		

Links

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

Crossrefs

Intersection of A000384 with A007504.

Subsequence of A066527.

Cf. A061890, A364691, A364694, A366270 (corresponding k values).

Programs

Mathematica

A366269list[kmax_]:=Module[{p=0},Join[{0},Table[If[IntegerQ[(Sqrt[8(p+=Prime[k])+1]+1)/4],p,Nothing],{k,kmax}]]];A366269list[10^5]

Formula

a(n) = A007504(A366270(n)).