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