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%I #16 Nov 17 2020 23:06:46
%S 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,
%T 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,
%U 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
%N Length (>1) of shortest sequence of consecutive primes starting with prime(n) whose sum is also prime, or -1 if no such sequence exists.
%H Charles R Greathouse IV, <a href="/A071194/b071194.txt">Table of n, a(n) for n = 1..10000</a>
%e For n=1, start-prime = prime(1) = 2, 2+3=5 is prime, length=2, so a(1)=2;
%e 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;
%e for n=160, prime(160) = 941, 941 + ... + 1609 = 121123 is prime, a(160)=95.
%t 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 *)
%o (PARI) a(n,p=prime(n))=my(q=p,t=2); while(!isprime(p+=q=nextprime(q+1)),t++);t
%o apply(p->a(0,p), primes(30)) \\ _Charles R Greathouse IV_, Jun 16 2015
%Y Cf. A071195, A071196, A071197, A071198.
%K nonn
%O 1,1
%A _Labos Elemer_, May 16 2002
%E Escape clause added by _N. J. A. Sloane_, Nov 17 2020
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