A071194 Length (>1) of shortest sequence of consecutive primes starting with prime(n) whose sum is also prime, or -1 if no such sequence exists.

2, 9, 3, 3, 3, 5, 3, 3, 3, 3, 3, 9, 3, 5, 7, 3, 5, 3, 3, 3, 5, 3, 3, 7, 7, 3, 7, 5, 3, 5, 5, 9, 5, 3, 3, 5, 3, 3, 11, 9, 5, 21, 5, 9, 3, 9, 3, 5, 55, 3, 7, 27, 9, 27, 7, 5, 5, 3, 9, 3, 3, 3, 5, 3, 7, 7, 11, 3, 3, 3, 5, 5, 7, 7, 3, 5, 3, 9, 3, 3, 5, 11, 3, 5, 47, 5, 3, 3, 5, 3, 3, 5, 7, 3, 3, 7, 3, 5, 5, 5, 3

Offset: 1

Author

Labos Elemer, May 16 2002

Keywords

• nonn

Examples

			For n=1, start-prime = prime(1) = 2, 2+3=5 is prime, length=2, so a(1)=2;
for n=2, start-prime = prime(2) = 3, 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127 is prime, length=9, all shorter partial sums are composite, so a(2)=9;
for n=160, prime(160) = 941, 941 + ... + 1609 = 121123 is prime, a(160)=95.
		

Links

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

Crossrefs

Cf. A071195, A071196, A071197, A071198.

Programs

Mathematica

Table[k = 2; While[CompositeQ@ Total@ Prime@ Range[n, n + k], k++]; k + 2 Boole[EvenQ@ k] - 1, {n, 120}] (* Michael De Vlieger, Jan 01 2017 *)

PARI

a(n,p=prime(n))=my(q=p,t=2); while(!isprime(p+=q=nextprime(q+1)),t++);t
apply(p->a(0,p), primes(30)) \\ Charles R Greathouse IV, Jun 16 2015

Extensions

Escape clause added by N. J. A. Sloane, Nov 17 2020