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A109801 Cumulative sum of squares of primes indexed by squares. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)