A321343 -id:A321343 - cp's OEIS frontend

A321342 Numbers k such that if j is the sum of the first k primes, then the sum of the first j primes is prime.

1, 9, 15, 19, 73, 85, 87, 103, 121, 157, 175, 277, 313, 317, 341, 357, 375, 385, 391, 421, 443, 447, 523, 525, 539, 571, 607, 611, 645, 701, 779, 783, 791, 799, 823, 831, 835, 853, 889, 907, 911, 925, 977, 1051, 1075, 1081, 1087, 1095, 1117, 1125, 1135, 1157, 1181, 1187, 1223, 1257, 1305, 1325

Offset: 1

David James Sycamore, Nov 06 2018

nonn

k is in the sequence if A007504(j) is prime, where j = A007504(k). A007504(j) must be odd to be prime, so j must be even and k must be odd. Therefore all terms are odd. The subsequence of primes is A321343.

			A007504(1) = 2 and A007504(2) = 5, a prime therefore 1 is a term.
A007504(3) = 10 and A007504(10) = 129, not prime, therefore 3 is not a term.
A007504(9) = 100 and A007504(100) = 24133, a prime so 9 is a term.

Ray Chandler, Table of n, a(n) for n = 1..16000
Daniel Suteu, Perl program

Cf. A007504, A013916, A321343.

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

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

sfp(n) = sum(k=1, n, prime(k)); \\ A007504
isok(n) = isprime(sfp(sfp(n))); \\ Michel Marcus, Nov 08 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

A321342 Numbers k such that if j is the sum of the first k primes, then the sum of the first j primes is prime.

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