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Search: id:A109801
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| A109801 |
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Cumulative sum of squares of primes indexed by squares. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Related to Prime(1^2) + prime(2^2) + ... + prime(n^2) (A109724).
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FORMULA
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(Prime[1^2])^2 + (prime[2^2])^2 + ... + (prime[n^2])^2. a(n+1) = a(n) + (A011757(n+1))^2.
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EXAMPLE
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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).
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CROSSREFS
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Cf. A000040, A000290, A000583, A011757, A109724, A109770.
Sequence in context: A009671 A015001 A111034 this_sequence A099340 A095210 A001545
Adjacent sequences: A109798 A109799 A109800 this_sequence A109802 A109803 A109804
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Aug 15 2005
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