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

1,1

Comments

k is a term if A007504(A007504(prime(k)) is prime. Terms can be even or odd since A007504(A007504(prime(k)) is odd for any k.

Links

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A007504, A013916, A321342, A321343.

Sequence in context: A182602 A123255 A053750 * A271921 A003249 A134862

Adjacent sequences: A321436 A321437 A321438 * A321440 A321441 A321442

Keyword

nonn

Author

David James Sycamore, Nov 09 2018

Extensions

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

Status

approved