Vincenzo Manto

A397067

Primes prime(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 15 2026

This sequence has been cited by and influenced 3 other sequences

Official Comments

Sequence Chart

Graph of A397067

Data

2,5,11,17,41,59,67,127,157,211,277,307,331,347,367,389,401,607,653,907,967,977,1153,1297,1567,1669,1697,1801,1873,2027,2221,2417,2659,2731,2749,2927,2963,3037,3517,3581,3593,3929,4007,4159,4217,4229,4339,4441

Formula

a(n) = A000040(A397068(n)).

Computational Implementations

PYTHON

from sympy import prime, isprime
def q(k):
    return isprime(sum(prime(i) for i in range(k, 2 * k)))
print([prime(k) for k in range(1, 501) if q(k)])

Mathematica

q[k_]:=PrimeQ[Sum[Prime[i],{i,k,k+k-1}]];Prime/@Select[Range[700],q]

Cross-References

See also OEIS entries: Cf A000040 A013917 A161463 A397068 A397069