

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.


3



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
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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[t1] + 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



