A397069 Primes equal to the sum of the k primes beginning with prime(k) for some k.

2, 23, 83, 197, 863, 1607, 2083, 6389, 9539, 16319, 27127, 31337, 35911, 38303, 43399, 48809, 51647, 108971, 127133, 226379, 252617, 259429, 357031, 443017, 624037, 714887, 726697, 812191, 863179, 998111, 1174519, 1399709, 1627357, 1757221, 1776277, 1992589

Offset

1,1

Comments

Subsequence of A161463.

Links

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

Formula

a(n) = A161463(A397068(n)).

a(n) = Sum_{i=A397068(n)..2*A397068(n)-1} A000040(i).

Example

5 is the third prime. The sum of the three primes beginning with 5 is 5 + 7 + 11 = 23, which is prime; therefore, 23 is a term.
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, 83 is a term.

Mathematica

q[k_]:=PrimeQ[Sum[Prime[i], {i, k, k+k-1}]]; fs[k_]:=Sum[Prime[i], {i, k, k+k-1}]; fs/@Select[Range[425], q]

Crossrefs

Cf. A000040, A013918, A161463, A397067, A397068.

Sequence in context: A209194 A097232 A339474 * A222564 A099134 A069152

Adjacent sequences: A397065 A397067 A397068 * A397070 A397072 A397073

Keyword

nonn,new

Author

James C. McMahon and Vincenzo Manto, Jun 17 2026

Status

approved