A397068 - OEIS

%I #10 Jun 24 2026 19:59:31

%S 1,3,5,7,13,17,19,31,37,47,59,63,67,69,73,77,79,111,119,155,163,165,

%T 191,211,247,263,265,279,287,307,331,359,385,399,401,423,427,435,491,

%U 501,503,545,553,573,577,579,593,603,611,617,637,665,671,707,723,735,739

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

%H James C. McMahon, <a href="/A397068/b397068.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 11 is the fifth prime. The sum of the five primes beginning with 11 is 11 + 13 + 17 + 19 + 23 = 83, which is prime; therefore, 5 is a term.

%e 3 is the second prime. The sum of the two primes beginning with 3 is 3 + 5 = 8, which is not prime; therefore, 2 is not a term.

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

%o (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

%Y Cf. A000040, A013916, A161463, A397067, A397069.

%K nonn

%O 1,2

%A _James C. McMahon_ and _Vincenzo Manto_, Jun 17 2026