A321343 Primes p such that if k is the sum of the first p primes then the sum of the first k primes is prime.

19, 73, 103, 157, 277, 313, 317, 421, 443, 523, 571, 607, 701, 823, 853, 907, 911, 977, 1051, 1087, 1117, 1181, 1187, 1223, 1451, 1453, 1531, 1667, 1861, 2551, 2999, 3169, 3257, 3389, 3583, 3671, 3889, 3907, 3911, 4597, 4691, 4919, 5347, 5527, 5569, 5623, 5657, 5839

Offset

1,1

Comments

Primes p such that A007504(A007504(p)) is prime; subsequence of A321342.

Links

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

Example

The smallest prime p such that A007504(p) is prime is 19 (sum of first 19 primes is 100 and sum of first 100 primes is 24133, which is prime). Therefore a(1) = 19.

Maple

N:=2000:
for n from 1 to N by 2 do
X:=add(ithprime(k), k=1..n);
Y:=add(ithprime(j), j=1..X);
if isprime(n)and isprime(Y) then print(n);
end if:
end do:

Mathematica

primeSum[n_] := Sum[Prime[i], {i, n}]; Select[Range[300], PrimeQ[#] && PrimeQ[primeSum[primeSum[#]]] &] (* Amiram Eldar, Nov 07 2018 *)

Prog

(PARI) upto(n) = {my(v = vector(n+1), res = List, t = 1, setv, s = 0, Ap = 0, AAp=0, q =0); v[1] = 2; forprime(p = 3, prime(n+1), t++; v[t] = v[t-1] + p); t=1; vt = v[1]; forprime(p = 2, , AAp += p; q++; if(q == vt, if(isprime(t) && isprime(AAp), listput(res, t); print1(t", ")); t++; if(t>=n, return(res)); vt = v[t])); res} \\ David A. Corneth, Nov 09 2018
(Perl)
use ntheory qw(:all);
for (my ($i, $k) = (1, 1); ; ++$k) {
    my $p = nth_prime($k);
    if (is_prime sum_primes nth_prime sum_primes nth_prime $p) {
        print "a($i) = $p\n"; ++$i;
    }
} # Daniel Suteu, Nov 11 2018

Crossrefs

Cf. A007504, A013916, A321439, A321342.

Sequence in context: A142516 A127874 A289817 * A255889 A154406 A141960

Adjacent sequences: A321340 A321341 A321342 * A321344 A321345 A321346

Keyword

nonn

Author

David James Sycamore, Nov 06 2018

Status

approved