A164041 Primes of the form 2*p^2 + 4*p + 1, where p is also prime.

17, 31, 71, 127, 647, 1151, 2887, 3527, 7687, 12799, 19207, 20807, 23327, 34847, 39199, 49927, 53791, 73727, 79999, 103967, 117127, 145799, 172871, 194687, 220447, 279751, 294911, 323207, 336199, 387199, 394271, 419527, 438047, 587527, 649799, 724807

Offset: 1

Author

Vincenzo Librandi, Aug 08 2009

Keywords

• nonn
• easy

Comments

A subsequence of the primes of the form 2k^2+4k+1 = 2*(k+1)^2-1, A066436. - R. J. Mathar, Aug 10 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[a: p in PrimesUpTo(700)|IsPrime(a) where a is 2*p^2+4*p+1 ] // Vincenzo Librandi, Sep 01 2012

Mathematica

lst={}; Do[p=Prime@n; a=2*p^2+4*p+1; If[PrimeQ@a,AppendTo[lst,a]],{n,7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *)
Select[Table[2p^2+4p+1,{p,Prime[Range[200]]}],PrimeQ] (* Harvey P. Dale, Aug 25 2019 *)

PARI

lista(nn) = {forprime(p=2, nn, if(isprime(q=2*p^2+4*p+1), print1(q, ", ")));} \\ Altug Alkan, Mar 29 2018

Formula

a(n) = 2*(A164042(n))^2 + 4*A164042(n) + 1.

Extensions

a(29) corrected by R. J. Mathar, Aug 11 2009

Edited by N. J. A. Sloane, Aug 11 2009