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 A163420 Primes p such that p+(p^2-1)/4 is also prime. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS J. Mulder, Table of n, a(n) for n = 1..50000 FORMULA A163419(n) = a(n)+( a(n)^2-1 )/4. [R. J. Mathar, Aug 17 2009] {A000040(k): A000040(k)+A024701(k-1) in A000040}. EXAMPLE 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. MATHEMATICA 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 *) PROG (Magma) [p: p in PrimesInInterval(3, 1000) | IsPrime(p+(p^2-1) div 4)]; // Vincenzo Librandi, Apr 08 2013 CROSSREFS Cf. A162652, A163418, A165350, A163419. Sequence in context: A342692 A048184 A290283 * A155489 A194099 A045396 Adjacent sequences: A163417 A163418 A163419 * A163421 A163422 A163423 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Jul 27 2009 EXTENSIONS Definition simplified by R. J. Mathar, Aug 17 2009 STATUS approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)