A163427 Primes p such that (p+1)^3/8+(p-1)/2 is also prime.

5, 7, 13, 19, 29, 31, 41, 53, 71, 101, 103, 109, 173, 191, 199, 223, 229, 233, 239, 257, 269, 277, 331, 383, 397, 431, 491, 569, 571, 599, 619, 631, 719, 733, 751, 757, 761, 823, 857, 859, 863, 887, 907, 937, 967, 971, 977, 1009, 1019, 1063, 1069, 1123, 1163

Offset

1,1

Comments

Primes A000040(k) such that (A006254(k-1))^3+ A005097(k-1) is also prime.

Links

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

Formula

(a(n)+1)^3/8+(a(n)-1)/2 = A163426(n).

Example

For p=5, (5+1)^3/8+(5-1)/2=27+2=29, prime, which adds p=5 to the sequence.
For p=7, (7+1)^3/8+(7-1)/2=67, prime, which adds p=7 to the sequence.

Mathematica

f[n_]:=((p+1)/2)^3+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst
Select[Prime[Range[100]], PrimeQ[(# + 1)^3 / 8 + (# - 1) / 2]&] (* Vincenzo Librandi, Apr 09 2013 *)

Prog

(Magma) [p: p in PrimesInInterval(3, 1200) | IsPrime((p+1)^3 div 8+(p-1) div 2)]; // Vincenzo Librandi, Apr 09 2013

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426.

Sequence in context: A314327 A215804 A274242 * A215805 A339692 A164567

Adjacent sequences: A163424 A163425 A163426 * A163428 A163429 A163430

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Extensions

Edited by R. J. Mathar, Aug 24 2009

Status

approved