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A225195
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Primes p such that (p+nextprime(p))/2 is a perfect square.
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5
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3, 7, 61, 79, 139, 223, 317, 439, 619, 1087, 1669, 2593, 3593, 4093, 5179, 6079, 8461, 12541, 13687, 16633, 19037, 19597, 25261, 27211, 28219, 29581, 36857, 38011, 39199, 45361, 46649, 47521, 51977, 56167, 74527, 87013, 88801, 91807, 92413, 95479, 103681
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OFFSET
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1,1
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COMMENTS
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Primes for which average of two consecutive primes is a perfect square.
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LINKS
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EXAMPLE
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61 is in the list since (61+67)/2=64=8^2.
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MATHEMATICA
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Select[Prime[Range[10000]], IntegerQ[Sqrt[(# + NextPrime[#])/2]] &]
Select[Partition[Prime[Range[10000]], 2, 1], IntegerQ[Sqrt[Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Jan 12 2019 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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