A321439 Numbers k such that if j is the sum of the first prime(k) primes then the sum of the first j primes is prime.

8, 21, 27, 37, 59, 65, 66, 82, 86, 99, 105, 111, 126, 143, 147, 155, 156, 165, 177, 181, 187, 194, 195, 200, 230, 231, 242, 262, 284, 374, 430, 449, 460, 477, 502, 512, 539, 540, 541, 622, 634, 657, 707, 731, 735, 739, 745, 766, 767, 781, 784, 785, 791, 801

Offset: 1

Author

David James Sycamore, Nov 09 2018

Keywords

• nonn

Comments

Numbers k such that A007504(A007504(prime(k))) is prime. Terms can be even or odd since A007504(A007504(prime(k))) is odd for any k.

Examples

			8 is a term because prime(8) = 19, A007504(19) = 568, and A007504(568) = 1086557, which is prime.
2 is not a term since prime(2) = 3, A007504(3) = 10 and A007504(10) = 129, which is not prime.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A007504, A013916, A321342, A321343.

Programs

Maple

N:=100:
for n from 1 to N do
X:=add(ithprime(k),k=1..ithprime(n));
Y:=add(ithprime(r),r=1..X);
if isprime(Y)then print(n);
end if:
end do:

Mathematica

primeSum[n_] := Sum[Prime[i], {i, n}]; Select[Range[200], PrimeQ[ primeSum[primeSum[Prime[#]]]] &] (* Amiram Eldar, Nov 09 2018 *)

PARI

sumprimes(n)={my(p=0, s=0); for(i=1, n, p=nextprime(1+p); s+=p); s}
ok(k)={isprime(sumprimes(sumprimes(prime(k))))}
for(n=1, 100, if(ok(n),print1(n, ", "))) \\ Andrew Howroyd, Nov 11 2018

Perl

use ntheory qw(:all);
for (my ($i, $k) = (1, 1); ; ++$k) {
    if (is_prime sum_primes nth_prime sum_primes nth_prime nth_prime $k) {
        print "a($i) = $k\n"; ++$i;
    }
} # Daniel Suteu, Nov 11 2018

Extensions

a(30)-a(54) from Daniel Suteu, Nov 11 2018