A163425 Primes p such that (p-1)^3/8+(p+1)^2/4 is also prime.

3, 5, 7, 17, 19, 29, 31, 47, 61, 71, 79, 101, 131, 167, 181, 197, 199, 227, 251, 269, 281, 307, 359, 397, 421, 449, 461, 467, 509, 569, 659, 691, 709, 811, 859, 919, 937, 997, 1031, 1087, 1151, 1217, 1231, 1249, 1277, 1279, 1301, 1307, 1361, 1409, 1447, 1451

Offset

1,1

Comments

The associated (p-1)^3/8+(p+1)^2/4 are in A163424.

Links

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

Example

p=3 is in the sequence because (3-1)^3/8+(3+1)^2/4=1+4=5 is also prime.
p=5 is in the sequence because (5-1)^3/8+(5+1)^2/4=17 is also prime.

Mathematica

f[n_]:=((p-1)/2)^3+((p+1)/2)^2; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 7!}]; lst
Select[Prime[Range[1500]], PrimeQ[(# - 1)^3 / 8 + (# + 1)^2 / 4]&] (* Vincenzo Librandi, Apr 08 2013 *)

Prog

(Magma) [p: p in PrimesInInterval(3, 2000) | IsPrime((p-1)^3 div 8 + (p+1)^2 div 4)]; // Vincenzo Librandi, Apr 08 2013

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422.

Sequence in context: A038971 A210479 A045400 * A191038 A299298 A122395

Adjacent sequences: A163422 A163423 A163424 * A163426 A163427 A163428

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Extensions

Comment turned into examples by R. J. Mathar, Sep 02 2009

Status

approved