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Search: id:A133557
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| A133557 |
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Numbers n for which sum of squares of five consecutive primes is prime A133558 . |
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+0
1
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| 2, 3, 9, 10, 11, 16, 18, 25, 26, 28, 31, 33, 36, 42, 43, 46, 47, 54, 56, 58, 63, 68, 76, 87, 91, 93, 99, 101, 105, 106, 114, 127, 131, 145, 153, 159, 183, 186, 196, 201, 206, 229, 230, 232, 233, 238, 239, 241, 244, 245, 246, 248, 253, 256, 257, 264, 265, 266, 268
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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 n=1 give prime. For sum of squares of three consecutive primes A133529 seems only n=2 give prime (checked for all n<1000000). Sums of squares of four (and all even number) of consecutive primes are even numbers with exception n=1.
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EXAMPLE
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a(2)=2 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, n]], {n, 1, 100}]; b {*Artur Jasinski*)
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CROSSREFS
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Cf. A133538, A133558.
Sequence in context: A007316 A135204 A037463 this_sequence A047475 A039012 A057291
Adjacent sequences: A133554 A133555 A133556 this_sequence A133558 A133559 A133560
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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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