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Search: id:A133559
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| A133559 |
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Primes which have partition as sum of squares of five consecutive primes. |
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4
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| 373, 653, 5381, 6701, 8069, 19541, 24821, 53549, 56909, 69389, 93581, 107741, 131837, 184901, 196661, 237821, 252509, 344021, 370661, 395069, 498989, 609269, 783701, 1055429, 1174781, 1239341, 1492637, 1576229, 1713989, 1749149, 2024261
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OFFSET
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1,1
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COMMENT
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For sum of squares of two consecutive primes only 2^2+3^2=13 is prime. For sum of squares of three consecutive primes A133529 seems that only 83 belonging(checked for all n<1000000). Sums of squares of four (and all even number) of consecutive primes are even numbers with exception n=1 but 2^2+3^2+5^2+7^2=87=3*29 is not prime.
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EXAMPLE
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a(2)=653 because Prime[2]^2+Prime[3]^2+Prime[4]^2+Prime[5]^2+Prime[6]^2=3^2+5^2+7^2+11^2+13^2=653 is prime
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MATHEMATICA
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b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b {*Artur Jasinski*)
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CROSSREFS
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Cf. A133538, A133558.
Sequence in context: A139659 A142395 A142921 this_sequence A023313 A134161 A168168
Adjacent sequences: A133556 A133557 A133558 this_sequence A133560 A133561 A133562
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Sep 16 2007
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