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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
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
Sequence in context: A342692 A048184 A290283 * A155489 A194099 A045396
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition simplified by R. J. Mathar, Aug 17 2009
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)