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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved