A071195 Final prime in sequence of primes starting with prime(n) and having prime sum (see A071194), or -1 if no such sequence exists.

3, 29, 11, 13, 17, 29, 23, 29, 31, 37, 41, 71, 47, 61, 73, 61, 73, 71, 73, 79, 97, 89, 97, 113, 127, 107, 137, 131, 127, 139, 149, 173, 157, 151, 157, 173, 167, 173, 227, 223, 197, 293, 211, 239, 211, 251, 227, 239, 563, 239, 269, 397, 283, 409, 283, 281, 283

Offset: 1

Author

Labos Elemer, May 16 2002

Keywords

• nonn

Comments

The length of the sequence is given in A071194.

Examples

			n=2: p(2)=3, 3+7+11+13+17+19+23+29 = 127 is the shortest partial sum with initial prime 3; it ends with p(10) = 29 = a(2);
n=6: p(6)=13, 13+17+19+23+29 = 101, so the end-prime = a(6) = 29.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071194, A071196, A071197, A071198.

Programs

Mathematica

Prime@ Table[k = 1; While[! PrimeQ@ Total@ Prime@ Range[n, n + k], k++]; n + k, {n, 57}] (* Michael De Vlieger, Mar 25 2017 *)

PARI

a(n,p=prime(n))=my(q=p); while(!isprime(p+=q=nextprime(q+1)),);q
apply(p->a(0,p), primes(30)) \\ Charles R Greathouse IV, Jun 16 2015

Extensions

Edited and escape clause added by N. J. A. Sloane, Nov 17 2020