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A163429 Primes p such that ((p+1)/2)^3+((p-1)/2)^2 is also prime. 3
5, 7, 11, 13, 29, 41, 53, 71, 73, 79, 97, 101, 131, 149, 179, 181, 193, 211, 227, 229, 239, 241, 269, 271, 293, 311, 313, 317, 337, 373, 401, 443, 461, 463, 503, 541, 569, 599, 601, 659, 673, 691, 769, 773, 809, 839, 857, 859, 863, 911, 919, 929, 971, 1009, 1019 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

((5+1)/2)^3+((5-1)/2)^2=27+4=31, ((7+1)/2)^3+((7-1)/2)^2=64+9=73,..

MATHEMATICA

f[n_]:=((p+1)/2)^3+((p-1)/2)^2; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst

Select[Prime[Range[200]], PrimeQ[((# + 1) / 2)^3 + ((# - 1) / 2)^2]&] (* Vincenzo Librandi, Apr 15 2013 *)

PROG

(MAGMA) [p: p in PrimesUpTo(1100) | IsPrime(((p+1)div 2)^3+((p-1)div 2)^2)]; // Vincenzo Librandi, Apr 15 2013

CROSSREFS

Cf. A168297, A163428, A163424.

Sequence in context: A180946 A265006 A135930 * A339953 A220951 A136055

Adjacent sequences:  A163426 A163427 A163428 * A163430 A163431 A163432

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)