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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A168297, A163428, A163424.

Sequence in context: A180946 A265006 A135930 * A339953 A220951 A136055

Adjacent sequences: A163426 A163427 A163428 * A163430 A163431 A163432

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Status

approved