A164042 Primes p such that 2*p^2+4*p+1 is also prime.

2, 3, 5, 7, 17, 23, 37, 41, 61, 79, 97, 101, 107, 131, 139, 157, 163, 191, 199, 227, 241, 269, 293, 311, 331, 373, 383, 401, 409, 439, 443, 457, 467, 541, 569, 601, 607, 619, 653, 709, 719, 773, 839, 853, 881, 929, 947, 983, 1031, 1063, 1087, 1097, 1109, 1153, 1231, 1249

Offset: 1

Author

Vincenzo Librandi, Aug 08 2009

Keywords

• nonn
• easy

Comments

If a(k) is of the form 3·2^(h-1)-1 and 2*a(k)+1 is prime, then 2^h*a(k)*(2*a(k)+1) and 2^h*(2*a(k)^2+4*a(k)+1) are a pair of amicable numbers. - Vincenzo Librandi, Jun 09 2014

Links

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

Crossrefs

Cf. A164041.

Programs

Magma

[p: p in PrimesUpTo(1500) | IsPrime(2*p^2+4*p+1)]; // Vincenzo Librandi, Apr 08 2013

Mathematica

lst={}; Do[p=Prime@n; a=2*p^2+4*p+1; If[PrimeQ@a,AppendTo[lst,p]],{n,7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 12 2009 *)
Select[Range[2000], PrimeQ[#]&&PrimeQ[2 #^2 + 4 # + 1]&] (* Vincenzo Librandi, Apr 08 2013 *)
Select[Prime[Range[250]],PrimeQ[2#^2+4#+1]&] (* Harvey P. Dale, Sep 06 2022 *)

Extensions

Extended by R. J. Mathar, Aug 11 2009