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Search: id:A133561
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| A133561 |
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Numbers n for which sum of squares of seven consecutive primes(n,n+1,n+2,n+3,n+4,n+5,n+6) is prime. |
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3
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| 3, 5, 6, 8, 9, 10, 14, 18, 19, 20, 21, 26, 32, 34, 37, 38, 39, 41, 44, 47, 49, 52, 53, 54, 59, 60, 63, 64, 66, 68, 70, 71, 75, 83, 88, 89, 91, 92, 97, 100, 107, 108, 110, 112, 113, 117, 122, 125, 128, 129, 131, 135, 141, 142, 150, 151, 157, 158, 165, 168, 169, 178, 183
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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. Sums of squares of five of consecutive primes A133559. Sums of squares of seven of consecutive primes A133562
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EXAMPLE
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a(3)=6 because Prime[6]^2+Prime[7]^2+Prime[8]^2+Prime[9]^2+Prime[10]^2+Prime[11]^2+Prime[12]^2=
13^2+17^2+19^2+23^2+29^2+31^2+37^2=4519 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 + Prime[n + 5]^a + Prime[n + 6]^a; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 100}]; b {*Artur Jasinski*)
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CROSSREFS
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Cf. A133538, A133558, A133559, A133561.
Sequence in context: A026430 A002150 A153264 this_sequence A095117 A089585 A121506
Adjacent sequences: A133558 A133559 A133560 this_sequence A133562 A133563 A133564
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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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