A370111 Least prime p such that the sum of 2i - 1 consecutive primes starting with p is prime for each i <= n and not prime for i = n+1, and -1 if no such prime exists.
2, 17, 5, 19, 29, 4831, 1235791, 61483, 126064739, 32485822049
Offset: 1
Examples
a(1) = 2: This is because the sum of 1 consecutive prime number starting with 2 (which is just 2 itself) is also a prime number. Additionally, the sum of 2 * 2 - 1 = 3 consecutive primes starting with 2 (i.e., 2 + 3 + 5 = 10 = 2 * 5) is not prime, and no smaller prime number satisfies this condition. a(2) = 17: 17 is prime and the sum of 2*2 - 1 = 3 consecutive primes starting with 17 (i.e., 17 + 19 + 23 = 59) is a prime number. However, the sum of 2 * 3 - 1 = 5 consecutive primes starting with 17 (i.e., 17 + 19 + 23 + 29 + 31 = 119 = 7 * 17) is not prime, and no lesser prime number meets this requirement.
Crossrefs
Cf. A370139.
Programs
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PARI
card(p)=my(c=0,q=p,s=q);while(isprime(s),c++;for(i=1,2,q=nextprime(q+2);s+=q));c a(n)=if(n==1,return(2));forprime(p=3,+oo,my(x=card(p));if(x==n,return(p)))