%I
%S 5,7,11,13,29,41,53,71,73,79,97,101,131,149,179,181,193,211,227,229,
%T 239,241,269,271,293,311,313,317,337,373,401,443,461,463,503,541,569,
%U 599,601,659,673,691,769,773,809,839,857,859,863,911,919,929,971,1009,1019
%N Primes p such that ((p+1)/2)^3+((p1)/2)^2 is also prime.
%H Vincenzo Librandi, <a href="/A163429/b163429.txt">Table of n, a(n) for n = 1..1000</a>
%e ((5+1)/2)^3+((51)/2)^2=27+4=31, ((7+1)/2)^3+((71)/2)^2=64+9=73,..
%t f[n_]:=((p+1)/2)^3+((p1)/2)^2; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,p]],{n,6!}];lst
%t Select[Prime[Range[200]], PrimeQ[((# + 1) / 2)^3 + ((#  1) / 2)^2]&] (* _Vincenzo Librandi_, Apr 15 2013 *)
%o (MAGMA) [p: p in PrimesUpTo(1100)  IsPrime(((p+1)div 2)^3+((p1)div 2)^2)]; // _Vincenzo Librandi_, Apr 15 2013
%Y Cf. A168297, A163428, A163424.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009
