A071151 Primes which are the sum of the first k odd primes for some k.

3, 127, 379, 499, 6079, 6599, 8273, 9521, 11597, 13099, 22037, 33623, 34913, 49279, 52517, 54167, 64613, 92951, 101999, 116531, 182107, 222269, 225829, 240379, 255443, 283079, 356387, 360977, 448867, 535669, 541339, 552751, 611953, 624209

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Analogous to A013918.

Cf. A013916-A013918, A065091, A071148-A071150, A007504.

Programs

Mathematica

s=0;lst={};Do[p=Prime[n];s+=p;If[PrimeQ[s],AppendTo[lst,s]],{n,2,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[Accumulate[Prime[Range[2,500]]],PrimeQ]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

list(lim)=my(v=List(),s); forprime(p=3,, if((s+=p)>lim, return(Vec(v))); if(isprime(s), listput(v,s))) \\ Charles R Greathouse IV, May 22 2017

Python

from sympy import isprime, nextprime; m = 0; p = 2
while p < 3100:
    p = nextprime(p); m += p
    if isprime(m): print(m, end = ', ') # Ya-Ping Lu, Dec 24 2024

Extensions

Name simplified by Charles R Greathouse IV, May 22 2017