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

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Comments

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

Examples

			((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.
		

Links

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

Crossrefs

Cf. A002327, A162652, A163418.

Programs

Magma

[a: p in PrimesInInterval(3, 600) | IsPrime(a) where a is (p^2 + 4*p - 1) div 4]; // Vincenzo Librandi, Sep 17 2016

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 *)

PARI

lista(nn) = forprime(p=3, nn, if(isprime(P=(p^2+4*p-1)/4), print1(P, ", "))); \\ Altug Alkan, Sep 17 2016