A164042 - OEIS

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

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OFFSET

1,1

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

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 *)

PROG

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

CROSSREFS

Cf. A164041.

Sequence in context: A164134 A152184 A135948 * A248344 A060212 A107439

Adjacent sequences: A164039 A164040 A164041 * A164043 A164044 A164045