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
Keywords
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
Programs
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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
Comments