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A109136
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Even numbers that are not congruent to 1 mod 3 nor are squares nor are the sum of a prime and a square of a prime.
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1
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2, 8, 18, 24, 74, 170, 614, 704, 1010, 1164, 15054, 21774, 24476
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OFFSET
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1,1
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COMMENTS
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We conjecture that every sufficiently large even number is congruent to 1 mod 3, or is a square, or is a sum of a prime and a square of a prime. The numbers listed here are believed to be the only exceptions. This has been verified up to 100000000.
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LINKS
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MATHEMATICA
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okQ[n_]:=Mod[n, 3]!=1&&!IntegerQ[Sqrt[n]]&&Count[n-Prime[Range[ PrimePi[n]]], _?(PrimeQ[Sqrt[#]]&)]==0; Select[Range[0, 25000, 2], okQ] (* Harvey P. Dale, Nov 08 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Dmytro Taranovsky (dmytro(AT)mit.edu), Aug 17 2005
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STATUS
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approved
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