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

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Magma

[p: p in PrimesInInterval(3, 2000) | IsPrime((p-1)^3 div 8 + (p+1)^2 div 4)]; // Vincenzo Librandi, Apr 08 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,7!}];lst
Select[Prime[Range[1500]], PrimeQ[(# - 1)^3 / 8 + (# + 1)^2 / 4]&] (* Vincenzo Librandi, Apr 08 2013 *)

Extensions

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