A109801 Cumulative sum of squares of primes indexed by squares.

4, 53, 582, 3391, 12800, 35601, 87130, 183851, 359412, 652093, 1089014, 1772943, 2791024, 4214273, 6250602, 8871763, 12402404, 16994853, 22933822, 30446903, 39951792, 51930313, 66393122, 84125643, 105627412, 131140013, 161599374

Offset

1,1

Comments

Related to Prime(1^2) + prime(2^2) + ... + prime(n^2) (A109724).

Links

Table of n, a(n) for n=1..27.

Formula

(Prime[1^2])^2 + (prime[2^2])^2 + ... + (prime[n^2])^2. a(n+1) = a(n) + (A011757(n+1))^2.

Example

a(1) = 4 because (prime[1^2])^2 = (prime[1])^2 = 2^2.
a(2) = 53 because (prime[1^2])^2 + (prime[2^2])^2 = 2^2 + 7^2 = 4 + 49 = 53 (which is prime).
a(3) = 582 because (prime[1^2])^2 + (prime[2^2])^2 + (prime[3^2])^2 = 2^2 + 7^2 + 23^2 = 582.
a(4) = 582 because (prime[1^2])^2 + (prime[2^2])^2 + (prime[3^2])^2 + (prime[4^2])^2 = 2^2 + 7^2 + 23^2 + 53^2 = 3391 (which is prime).
a(32) = a(31) + (prime[32^2])^2 = 345995122 + 8161^2 = 412597043 (which is prime).
a(34) = a(33) + (prime[34^2])^2 = 488932212 + 9341^2 = 576186493 (which is prime).

Mathematica

Accumulate[Prime[Range[30]^2]^2] (* Harvey P. Dale, Mar 28 2012 *)

Crossrefs

Cf. A000040, A000290, A000583, A011757, A109724, A109770.

Sequence in context: A111034 A214367 A241872 * A099340 A221605 A307172

Adjacent sequences: A109798 A109799 A109800 * A109802 A109803 A109804

Keyword

nonn

Author

Jonathan Vos Post, Aug 15 2005

Status

approved