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A084951
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Primes in A075893: Primes of the form (p^2+q^2+r^2)/3, where p,q,r are 3 consecutive primes.
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9
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113, 193, 577, 1913, 2833, 10753, 44617, 48593, 54617, 69193, 74177, 78593, 86729, 102673, 107873, 122273, 156577, 183497, 214993, 228233, 247697, 308809, 334513, 414313, 581177, 602753, 617369, 636353, 691697, 861857, 1408993, 1786097
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OFFSET
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1,1
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COMMENTS
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With the exception of 2^2+3^2+5^2=38 and 3^2+5^2+7^2=83 all sums of squares of 3 consecutive primes are divisible by 3 because mod(p^2,3)=1 for all primes p>3.
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LINKS
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EXAMPLE
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a(1)=113 because (7^2+11^2+13^2)/3=(49+121+169)/3=339/3=113 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)/3; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 200}]; b (* Artur Jasinski, Sep 30 2007 *)
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PROG
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(PARI) v=vector(10000); i=0; p=5; q=7; forprime(r=8, 1e8, if(isprime(t=(p^2+q^2+r^2)/3), v[i++]=t; if(i==#v, return)); p=q; q=r) \\ Charles R Greathouse IV, Feb 14 2011
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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