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A163420
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Primes p such that p+(p^2-1)/4 is also prime.
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11
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3, 5, 7, 11, 17, 19, 29, 31, 37, 41, 47, 59, 61, 89, 107, 109, 127, 131, 139, 151, 191, 199, 227, 229, 239, 251, 281, 307, 317, 337, 347, 359, 367, 389, 397, 439, 449, 461, 479, 487, 491, 569, 587, 601, 617, 659, 661, 677, 701, 719, 727, 769, 809, 839, 911, 941
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OFFSET
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1,1
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LINKS
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FORMULA
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A163419(n) = a(n)+( a(n)^2-1 )/4. [R. J. Mathar, Aug 17 2009]
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EXAMPLE
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3 is in the sequence because 3+(3^2-1)/4=5 is a prime number.
5 is in the sequence because 5+(5^2-1)/4=11 is a prime number.
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MATHEMATICA
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f[n_]:=((p+1)/2)^2+((p-1)/2); lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 6!}]; lst
Select[Range[700], PrimeQ[#] && PrimeQ[# + (#^2 - 1)/4] &] (* Vincenzo Librandi, Apr 08 2013 *)
Select[Prime[Range[200]], PrimeQ[#+(#^2-1)/4]&] (* Harvey P. Dale, Jun 18 2014 *)
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PROG
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(Magma) [p: p in PrimesInInterval(3, 1000) | IsPrime(p+(p^2-1) div 4)]; // 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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