A122207 Primes of the form A109724[n] = A007504[n^2] or the sum of the first n^2 primes.

2, 17, 8893, 24133, 768373, 1583293, 2180741, 3875933, 6426919, 173472547, 289093219, 741938801, 2738357903, 2895147163, 3058653607, 17056871941, 24109439269, 26602406177, 29286422621, 62073696299, 65420584637, 68902997299

Offset

1,1

Comments

Numbers n such that A109724[n] = A007504[n^2] is a prime are listed in A122208[n] = {1,2,8,10,22,26,28,32,36,78,88,110,150,152,154,...}.

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Formula

a(n) = A109724[ A122208[n] ] = A007504[ A122208[n]^2 ].

Example

Prime 17 = 2 + 3 + 5 + 7 = a(2) is equal to the sum of the first 4 = 2^2 primes.
Prime 24133 = a(4) is equal to sum of the first 100 = 10^2 primes.

Mathematica

s=0; Do[s=Sum[Prime[k], {k, 1, n^2}]; If[PrimeQ[s], Print[{n, n^2, s}]], {n, 1, 154}]
Select[Table[Total[Prime[Range[n^2]]], {n, 500}], PrimeQ] (* Harvey P. Dale, Jul 20 2024 *)

Crossrefs

Cf. A122208, A109724, A007504.

Sequence in context: A279884 A060353 A002814 * A174305 A003819 A078624

Adjacent sequences: A122204 A122205 A122206 * A122208 A122209 A122210

Keyword

nonn

Author

Alexander Adamchuk, Aug 25 2006

Extensions

More terms from Ray Chandler, Dec 02 2018

Status

approved