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A075893
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Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.
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4
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65, 113, 193, 273, 393, 577, 777, 1057, 1337, 1633, 1913, 2289, 2833, 3337, 3897, 4417, 4953, 5537, 6153, 7017, 8073, 9177, 10073, 10753, 11313, 12033, 13593, 15353, 17353, 18417, 20097, 21441, 23217, 24673, 26369, 28129, 29953, 31577, 33761
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OFFSET
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3,1
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COMMENTS
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Unlike the average of three successive primes, the average of three successive primes (greater than 3) squared is always integral.
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LINKS
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FORMULA
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a(n) = (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.
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EXAMPLE
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a(3)=65 because (prime(3)^2+prime(4)^2+prime(5)^2)/3=(5^2+7^2+11^2)/3=65.
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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; AppendTo[b, k], {n, 3, 50}]; b (* Artur Jasinski, Sep 30 2007 *)
Mean[#]&/@Partition[Prime[Range[3, 50]]^2, 3, 1] (* Harvey P. Dale, Jun 09 2013 *)
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PROG
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(Magma) [(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2)/3: n in [3..50]]; // Vincenzo Librandi, Aug 21 2018
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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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