A013917 a(n) is prime and sum of all primes <= a(n) is prime.

2, 3, 7, 13, 37, 43, 281, 311, 503, 541, 557, 593, 619, 673, 683, 733, 743, 839, 881, 929, 953, 1061, 1163, 1213, 1249, 1277, 1283, 1307, 1321, 1949, 2029, 2161, 2203, 2213, 2237, 2243, 2297, 2357, 2393, 2411, 2957, 3137, 3251, 3257, 3301, 3413, 3461, 3491

Offset: 1

Author

N. J. A. Sloane, Renaud Lifchitz (100637.64(AT)CompuServe.COM)

Keywords

• nonn

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000
• Romeo Meštrović, Curious conjectures on the distribution of primes among the sums of the first 2n primes, arXiv:1804.04198 [math.NT], 2018.

Crossrefs

Cf. A013916, A013918.

Programs

Mathematica

Prime[Flatten[Position[Accumulate[Prime[Range[500]]], ?PrimeQ]]] (* _Jayanta Basu, May 18 2013 *)

PARI

isA013917(n) = isprime(n) && isprime(sum(i=2,n,isprime(i)*i)) \\ Michael B. Porter, Jan 29 2010

PARI

list(lim)=my(v=List(),s); forprime(p=2,lim, if(isprime(s+=p), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Oct 19 2021

Formula

a(n) = A000040(A013916(n)).

Extensions

More terms from David W. Wilson