A307470 Intersection of A013917 and A013918.

2, 281, 25237, 1359329, 1603597, 6706397, 8300797, 32106383, 33262057, 33312781, 37233373, 57922687, 87938423, 124285471, 143031971, 144784201, 179684179, 185763283, 186515239, 229240489, 237863777, 248536159, 280322407, 298010851, 375529801, 481405411, 488236271, 498472207

Offset: 1

Author

Torlach Rush, Apr 09 2019

Keywords

• nonn

Comments

For a number to be a term of this sequence it must satisfy two similar but distinct conditions:

1. The number is prime and is the sum of consecutive primes.

2. The sum of all primes up to and including the number is also a prime number.

See examples below.

Examples

			2 is a term because 2 is prime and equals Sum_{2}. This is the trivial case.
281 is a term because 281 is prime and equals Sum_{2,3,...,41,43}, also Sum_{2,3,...,41,43,47,...,277,281} = 7699 which is also prime.
		

Crossrefs

Cf. A013917, A013918.

Programs

PARI

listp(nn) = {my(s=0); forprime(p=2, nn, s += p; if (isprime(s), my(ss = 0); forprime(q=2, s, ss += q); if (isprime(ss), print1(s, ", "));););} \\ Michel Marcus, Apr 11 2019

Extensions

More terms from Michel Marcus, Apr 11 2019