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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A071195, A071196, A071197, A071198.

Sequence in context: A011240 A021345 A011066 * A347359 A346839 A137616

Adjacent sequences: A071191 A071192 A071193 * A071195 A071196 A071197

Keyword

nonn

Author

Labos Elemer, May 16 2002

Extensions

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

Status

approved