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Search: id:A133562
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| A133562 |
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Numbers which are sum of squares of seven consecutive primes(n,n+1,n+2,n+3,n+4,n+5,n+6). |
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2
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| 666, 1023, 1543, 2359, 3271, 4519, 6031, 7591, 9439, 11719, 14359, 17119, 20239, 23599, 27079, 31111, 35191, 39631, 45319, 51031, 56599, 62719, 68359, 74239, 82447, 90199, 98767, 107479, 118231, 129151, 141031, 151471, 162199, 173359
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OFFSET
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1,1
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COMMENT
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Primes among A133562 see A133560. 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; AppendTo[b, k]], {n, 1, 100}]; b {*Artur Jasinski*)
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CROSSREFS
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Cf. A133538, A133558, A133559, A133561.
Sequence in context: A105978 A069426 A093733 this_sequence A062045 A043515 A051003
Adjacent sequences: A133559 A133560 A133561 this_sequence A133563 A133564 A133565
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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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