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Numbers n such that composite (n) + n is a prime, where composite (n) denotes the n-th composite number.
1

%I #8 Nov 21 2013 12:49:38

%S 1,3,4,8,11,27,29,40,44,45,47,57,58,66,69,71,83,84,90,100,103,108,111,

%T 116,117,127,133,135,136,144,147,151,153,156,160,163,176,179,197,201,

%U 211,214,216,221,239,242,251,252,255,260,263,269,272,274,275,280,287

%N Numbers n such that composite (n) + n is a prime, where composite (n) denotes the n-th composite number.

%C 8 is in the list because composite(8) + 8 = 15 + 8 = 23 is prime.

%C 27 is in the list because composite(27) + 27 = 40 + 27 = 67 is prime.

%t nn=400;With[{cnos=Rest[Complement[Range[nn],Prime[Range[PrimePi[nn]]]]]}, Transpose[Select[Thread[{cnos,Range[Length[cnos]]}], PrimeQ[Total[#]]&]][[2]]] (* _Harvey P. Dale_, Mar 24 2011 *)

%Y Cf. A002808.

%Y Complement of A161539.

%K nonn

%O 1,2

%A _Claudio Meller_, Jun 13 2009