A163424 Primes of the form (p-1)^3/8 + (p+1)^2/4 where p is prime.

5, 17, 43, 593, 829, 2969, 3631, 12743, 27961, 44171, 60919, 127601, 278981, 578843, 737281, 950993, 980299, 1455893, 1969001, 2424329, 2763881, 3605293, 5767739, 7801993, 9305521, 11290049, 12220361, 12704093, 16452089, 22987529, 35720189

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1100

Example

(3-1)^3/8 + (3+1)^2/4 = 1 + 4 = 5;
(5-1)^3/8 + (5+1)^2/4 = 8 + 9 = 17;
(7-1)^3/8 + (7+1)^2/4 = 27 + 16 = 43.

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, 7!}]; lst
Select[(#-1)^3/8+(#+1)^2/4&/@Prime[Range[150]], PrimeQ] (* Harvey P. Dale, Oct 05 2018 *)

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=3, , t=((p-1)/2)^3 + ((p+1)/2)^2; if(t>lim, break); if(isprime(t), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Dec 23 2016

Crossrefs

Subsequence of A100662.

For the corresponding primes p, see A163425.

Cf. A162652, A163418, A163419, A163420, A163421, A163422.

Sequence in context: A146778 A146858 A146183 * A294102 A190969 A099451

Adjacent sequences: A163421 A163422 A163423 * A163425 A163426 A163427

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Status

approved