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A109136 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. 1

%I #4 Nov 08 2012 09:28:39

%S 2,8,18,24,74,170,614,704,1010,1164,15054,21774,24476

%N 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.

%C 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.

%t 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 *)

%K nonn

%O 1,1

%A Dmytro Taranovsky (dmytro(AT)mit.edu), Aug 17 2005

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