A364691 Pentagonal numbers which are the sum of the first k primes, for some k >= 0.

0, 5, 13490, 3299391550, 22042432252064127, 2387505511919644051, 680588297594638712735

Offset

1,2

Links

Table of n, a(n) for n=1..7.

Wikipedia, Pentagonal number.

Index to sequences related to polygonal numbers

Example

5 is a term because it's both a pentagonal number and the sum of the first two primes (2 + 3).

Mathematica

A364691list[kmax_]:=Module[{p=0}, Join[{0}, Table[If[IntegerQ[(Sqrt[24(p+=Prime[k])+1]+1)/6], p, Nothing], {k, kmax}]]]; A364691list[25000] (* Paolo Xausa, Oct 06 2023 *)

Prog

(PARI) ispenta(n) = my(s); issquare(24*n+1, &s)&&s%6==5;
my(S=0); forprime (p=2, oo, S+=p; if (ispenta(S), print1(S, ", "))) \\ Hugo Pfoertner, Aug 03 2023

Crossrefs

Intersection of A000326 with A007504.

Cf. A066527, A061890, A364694, A364696, A366269.

Sequence in context: A058051 A242772 A368067 * A367943 A089989 A219011

Adjacent sequences: A364688 A364689 A364690 * A364692 A364693 A364694

Keyword

nonn,hard,more

Author

Paolo Xausa, Aug 03 2023

Extensions

a(5)-a(7) from Hugo Pfoertner, Aug 04 2023

Status

approved