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Numbers not expressed in form pi(n)+pi(sqrt(n)) with prime n.
1

%I #13 Aug 03 2014 14:01:26

%S 3,6,12,19,35,45,68,80,108,156,173,231,276,297,344,425,504,537,628,

%T 695,726,833,909,1024,1188,1278,1321,1409,1452,1553,1908,2008,2174,

%U 2224,2524,2583,2766,2953,3082,3281,3477,3554,3911,3989,4134,4210,4674,5154,5323

%N Numbers not expressed in form pi(n)+pi(sqrt(n)) with prime n.

%C Or places of squares in A000430.

%e 12 is in the sequence, since pi(23)+pi(sqrt(23))=9+2=11, while pi(29)+pi(sqrt(29))=10+3=13.

%e Also 12 is in the sequence since A000430(12)=25 is not prime.

%t t = Table[PrimePi[n] + PrimePi[Sqrt[n]], {n, Prime[Range[10000]]}]; Complement[Range[t[[-1]]], t] (* _T. D. Noe_, Apr 09 2012 *)

%Y Cf. A000430, A000040.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Apr 06 2012