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A164042
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Primes p such that 2*p^2+4*p+1 is also prime.
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2
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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
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(Magma) [p: p in PrimesUpTo(1500) | IsPrime(2*p^2+4*p+1)]; // Vincenzo Librandi, Apr 08 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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