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A164042
Primes p such that 2*p^2+4*p+1 is also prime.
2
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
1,1
COMMENTS
If a(k) is of the form 3ยท2^(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
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 08 2009
EXTENSIONS
Extended by R. J. Mathar, Aug 11 2009
STATUS
approved