A163419 Primes of the form ((p+1)/2)^2+((p-1)/2), where p is prime.

5, 11, 19, 41, 89, 109, 239, 271, 379, 461, 599, 929, 991, 2069, 2969, 3079, 4159, 4421, 4969, 5851, 9311, 10099, 13109, 13339, 14519, 16001, 20021, 23869, 25439, 28729, 30449, 32579, 34039, 38219, 39799, 48619, 50849, 53591, 57839, 59779, 60761

Offset

1,1

Comments

Subsequence of A002327. - Charles R Greathouse IV, Aug 11 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Example

((3+1)/2)^2+((3-1)/2) = 4+1 = 5;
((5+1)/2)^2+((5-1)/2) = 9+2 = 11;
((7+1)/2)^2+((7-1)/2) = 16+3 = 19.

Mathematica

f[n_]:=((p+1)/2)^2+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, f[p]]], {n, 6!}]; lst
Select[((#+1)/2)^2+(#-1)/2&/@Prime[Range[500]], PrimeQ] (* Harvey P. Dale, Nov 25 2012 *)

Prog

(Magma) [a: p in PrimesInInterval(3, 600) | IsPrime(a) where a is (p^2 + 4*p - 1) div 4]; // Vincenzo Librandi, Sep 17 2016
(PARI) lista(nn) = forprime(p=3, nn, if(isprime(P=(p^2+4*p-1)/4), print1(P, ", "))); \\ Altug Alkan, Sep 17 2016

Crossrefs

Cf. A002327, A162652, A163418.

Sequence in context: A289530 A106016 A112794 * A371668 A337492 A236584

Adjacent sequences: A163416 A163417 A163418 * A163420 A163421 A163422

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Status

approved