Vincenzo Manto

A397068

Numbers k such that the sum of the k primes beginning with prime(k) is prime.

Created: 6/24/2026 | Author: James C. McMahon and Vincenzo Manto , Jun 17 2026

This sequence has been cited by and influenced 3 other sequences

Official Comments

Sequence Chart

Graph of A397068

Data

1,3,5,7,13,17,19,31,37,47,59,63,67,69,73,77,79,111,119,155,163,165,191,211,247,263,265,279,287,307,331,359,385,399,401,423,427,435,491,501,503,545,553,573,577,579,593,603,611,617,637,665,671,707,723,735,739

Formula

A397067(n) = A000040(a(n)).

Computational Implementations

PARI

isok(k) = my(v2 = primes(2*k-1), v1 = Vec(v2, k-1)); if (k==1, v1=[]); isprime(vecsum(v2)-vecsum(v1)); \\ _Michel Marcus_, Jun 19 2026

Mathematica

q[k_]:=PrimeQ[Sum[Prime[i], {i, k, k+k-1}]];Select[Range[750], q]

Cross-References

See also OEIS entries: Cf A000040 A013916 A161463 A397067 A397069