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Search: id:A133560
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| A133560 |
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Primes which have partition as sum of squares of the seven consecutive primes. |
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2
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| 1543, 3271, 4519, 7591, 9439, 11719, 23599, 39631, 45319, 51031, 56599, 90199, 151471, 173359, 210319, 222919, 235159, 261463, 313879, 367711, 402511, 459223, 478831, 499711, 610567, 634327, 732967, 760519, 819319, 883087, 939439, 968959
(list; graph; listen)
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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 isn't prime. Sums of squares of five of consecutive primes A133559.
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EXAMPLE
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a(3)=4519 because 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, k]], {n, 1, 100}]; b {*Artur Jasinski*)
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CROSSREFS
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Cf. A133538, A133558, A133559, A133561.
Sequence in context: A092717 A083734 A137598 this_sequence A038009 A090209 A020408
Adjacent sequences: A133557 A133558 A133559 this_sequence A133561 A133562 A133563
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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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