A163422 Primes p such that A071568((p-1)/2) is also prime.

3, 5, 7, 11, 13, 17, 19, 31, 37, 43, 59, 61, 79, 83, 89, 97, 107, 109, 113, 139, 149, 167, 191, 233, 241, 263, 271, 293, 307, 311, 337, 359, 373, 383, 439, 443, 479, 487, 491, 523, 557, 617, 641, 647, 659, 673, 683, 701, 733, 757, 811, 829, 853, 857, 859, 877

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Comments

Primes p such that (p-1)^3/8+(p+1)/2 is also prime, i.e., in A095692.

Examples

			p=3 is in the sequence because (3-1)^3/8+(3+1)/2=3 is prime.
p=5 is in the sequence because (5-1)^3/8+(5+1)/2=11 is prime.
		

Links

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

Crossrefs

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

Programs

Magma

[p: p in PrimesUpTo(1000) | IsPrime((p^3-3*p^2+7*p+3) div 8)]; // Vincenzo Librandi, Apr 10 2013

Mathematica

f[n_]:=((n-1)/2)^3+((n+1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n,6!}]; lst
Select[Prime[Range[180]], PrimeQ[(#-1)^3/8+(#+1)/2]&]  (* Harvey P. Dale, Jan 05 2011 *)

Extensions

Definition rewritten by R. J. Mathar, Aug 17 2009