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

Author

David James Sycamore, Nov 06 2018

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A007504, A013916, A321343.

Programs

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 *)

PARI

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