A397068 Numbers k such that the sum of the k primes beginning with prime(k) is prime.

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

Offset

1,2

Links

James C. McMahon, Table of n, a(n) for n = 1..1000

Formula

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

Example

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.
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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A045398 A383680 A162565 * A321363 A355853 A155045

Adjacent sequences: A397063 A397065 A397067 * A397069 A397070 A397072

Keyword

nonn

Author

James C. McMahon and Vincenzo Manto, Jun 17 2026

Status

approved