A163420 Primes p such that p+(p^2-1)/4 is also prime.

3, 5, 7, 11, 17, 19, 29, 31, 37, 41, 47, 59, 61, 89, 107, 109, 127, 131, 139, 151, 191, 199, 227, 229, 239, 251, 281, 307, 317, 337, 347, 359, 367, 389, 397, 439, 449, 461, 479, 487, 491, 569, 587, 601, 617, 659, 661, 677, 701, 719, 727, 769, 809, 839, 911, 941

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Examples

			3 is in the sequence because 3+(3^2-1)/4=5 is a prime number.
5 is in the sequence because 5+(5^2-1)/4=11 is a prime number.
		

Links

• J. Mulder, Table of n, a(n) for n = 1..50000

Crossrefs

Cf. A162652, A163418, A165350, A163419.

Programs

Magma

[p: p in PrimesInInterval(3,1000) | IsPrime(p+(p^2-1) div 4)]; // Vincenzo Librandi, Apr 08 2013

Mathematica

f[n_]:=((p+1)/2)^2+((p-1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, p]],{n,6!}];lst
Select[Range[700], PrimeQ[#] && PrimeQ[# + (#^2 - 1)/4] &] (* Vincenzo Librandi, Apr 08 2013 *)
Select[Prime[Range[200]],PrimeQ[#+(#^2-1)/4]&] (* Harvey P. Dale, Jun 18 2014 *)

Formula

A163419(n) = a(n)+( a(n)^2-1 )/4. [R. J. Mathar, Aug 17 2009]

{A000040(k): A000040(k)+A024701(k-1) in A000040}.

Extensions

Definition simplified by R. J. Mathar, Aug 17 2009