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

1,2

Comments

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.

Links

Ray Chandler, Table of n, a(n) for n = 1..16000

Daniel Suteu, Perl program

Example

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.

Maple

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:

Mathematica

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

Prog

(PARI) sfp(n) = sum(k=1, n, prime(k)); \\ A007504
isok(n) = isprime(sfp(sfp(n))); \\ Michel Marcus, Nov 08 2018

Crossrefs

Cf. A007504, A013916, A321343.

Sequence in context: A058211 A038599 A330438 * A338599 A333312 A255763

Adjacent sequences: A321339 A321340 A321341 * A321343 A321344 A321345

Keyword

nonn

Author

David James Sycamore, Nov 06 2018

Status

approved