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

1,1

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A013916, A013918.

Sequence in context: A033995 A345247 A373894 * A371181 A293994 A196419

Adjacent sequences: A013914 A013915 A013916 * A013918 A013919 A013920

Keyword

nonn

Author

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

Extensions

More terms from David W. Wilson

Status

approved