A321342 -id:A321342 - cp's OEIS frontend

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

David James Sycamore, Nov 06 2018

nonn

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

			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.

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

Cf. A007504, A013916, A321439, A321342.

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:

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

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

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

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.

Original entry on oeis.org

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

David James Sycamore, Nov 09 2018

nonn

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.

			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.

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

Cf. A007504, A013916, A321342, A321343.

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:

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

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

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

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

cp's OEIS Frontend

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.

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