A163428 Primes of the form ((p+1)/2)^3 + ((p-1)/2)^2 where p is prime.

31, 73, 241, 379, 3571, 9661, 20359, 47881, 51949, 65521, 119953, 135151, 291721, 427351, 736921, 761671, 921889, 1202041, 1494313, 1533871, 1742161, 1785961, 2478331, 2533681, 3197839, 3820441, 3894229, 4044643, 4855033, 6573799

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Comments

Primes of the form k^3 + k^2 - 2k + 1 where 2k-1 is prime.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426, A163427

Programs

Maple

res:= NULL:
count:= 0:
p:= 2
while count < 100 do
  p:= nextprime(p);
  r:=  ((p+1)/2)^3 + ((p-1)/2)^2;
  if isprime(r) then
     res:= res, r;
     count:= count+1;
  fi
od:
res; # Robert Israel, Oct 10 2016

Mathematica

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

PARI

lista(nn) = forprime(p=3, nn, if (isprime(q=((p+1)/2)^3 + ((p-1)/2)^2), print1(q, ", "))); \\ Michel Marcus, Oct 11 2016

Extensions

Description and edits by Charles R Greathouse IV, Oct 05 2009