A163429 Primes p such that ((p+1)/2)^3+((p-1)/2)^2 is also prime.

5, 7, 11, 13, 29, 41, 53, 71, 73, 79, 97, 101, 131, 149, 179, 181, 193, 211, 227, 229, 239, 241, 269, 271, 293, 311, 313, 317, 337, 373, 401, 443, 461, 463, 503, 541, 569, 599, 601, 659, 673, 691, 769, 773, 809, 839, 857, 859, 863, 911, 919, 929, 971, 1009, 1019

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Examples

			((5+1)/2)^3+((5-1)/2)^2=27+4=31, ((7+1)/2)^3+((7-1)/2)^2=64+9=73,..
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A168297, A163428, A163424.

Programs

Magma

[p: p in PrimesUpTo(1100) | IsPrime(((p+1)div 2)^3+((p-1)div 2)^2)]; // Vincenzo Librandi, Apr 15 2013

Mathematica

f[n_]:=((p+1)/2)^3+((p-1)/2)^2; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[200]], PrimeQ[((# + 1) / 2)^3 + ((# - 1) / 2)^2]&] (* Vincenzo Librandi, Apr 15 2013 *)