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

1,1

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

Formula

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

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 *)

Prog

(Magma) [a: p in PrimesUpTo(700)|IsPrime(a) where a is 2*p^2+4*p+1 ] // Vincenzo Librandi, Sep 01 2012
(PARI) lista(nn) = {forprime(p=2, nn, if(isprime(q=2*p^2+4*p+1), print1(q, ", "))); } \\ Altug Alkan, Mar 29 2018

Crossrefs

Sequence in context: A087166 A167496 A370851 * A085598 A163443 A339181

Adjacent sequences: A164038 A164039 A164040 * A164042 A164043 A164044

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 08 2009

Extensions

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

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

Status

approved