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%I #20 Jul 04 2018 20:17:38
%S 2,3,7,12,18,21,36,37,42,45,52,55,60,61,65,68,70,79,84,95,98,113,130,
%T 135,143,145,155,180,181,185,195,205,216,222,231,239,253,262,273,275,
%U 325,332,334,354,368,370,385,402,417,421,432,433,454,462,488,505,516
%N Numbers n such that n^2 + pi(n) is prime.
%C Conjecture: the sequence is infinite.
%H K. D. Bajpai and Charles R Greathouse IV, <a href="/A228828/b228828.txt">Table of n, a(n) for n = 1..10000</a> (first 3000 terms from Bajpai)
%e a(6) = 21 : n^2+pi(n ) = 21^2 + pi(21) = 441+8 = 449 which is a prime.
%p with(numtheory): KD:= proc() local a; a:= n^2+pi(n); if isprime(a) then RETURN(n): fi; end: seq(KD(), n=1..2000);
%t Select[Range[600],PrimeQ[#^2+PrimePi[#]]&] (* _Harvey P. Dale_, Jul 04 2018 *)
%o (PARI) v=List(); p=0; for(n=2,1e4,p+=isprime(n); if(isprime(n^2+p), listput(v, n))); Vec(v) \\ _Charles R Greathouse IV_, Sep 04 2013
%Y Cf. A064711, A064712.
%Y Cf. A077510 (numbers n such that n + pi(n) is a prime).
%K nonn
%O 1,1
%A _K. D. Bajpai_, Sep 04 2013
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