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

1,1

Comments

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A081092 A291360 A269326 * A155055 A030096 A045394

Adjacent sequences: A163419 A163420 A163421 * A163423 A163424 A163425

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Extensions

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

Status

approved