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%I #15 Sep 08 2022 08:45:46
%S 3,5,7,11,17,19,29,31,37,41,47,59,61,89,107,109,127,131,139,151,191,
%T 199,227,229,239,251,281,307,317,337,347,359,367,389,397,439,449,461,
%U 479,487,491,569,587,601,617,659,661,677,701,719,727,769,809,839,911,941
%N Primes p such that p+(p^2-1)/4 is also prime.
%H J. Mulder, <a href="/A163420/b163420.txt">Table of n, a(n) for n = 1..50000</a>
%F A163419(n) = a(n)+( a(n)^2-1 )/4. [R. J. Mathar, Aug 17 2009]
%F {A000040(k): A000040(k)+A024701(k-1) in A000040}.
%e 3 is in the sequence because 3+(3^2-1)/4=5 is a prime number.
%e 5 is in the sequence because 5+(5^2-1)/4=11 is a prime number.
%t f[n_]:=((p+1)/2)^2+((p-1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, p]],{n,6!}];lst
%t Select[Range[700], PrimeQ[#] && PrimeQ[# + (#^2 - 1)/4] &] (* _Vincenzo Librandi_, Apr 08 2013 *)
%t Select[Prime[Range[200]],PrimeQ[#+(#^2-1)/4]&] (* _Harvey P. Dale_, Jun 18 2014 *)
%o (Magma) [p: p in PrimesInInterval(3,1000) | IsPrime(p+(p^2-1) div 4)]; // _Vincenzo Librandi_, Apr 08 2013
%Y Cf. A162652, A163418, A165350, A163419.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009
%E Definition simplified by _R. J. Mathar_, Aug 17 2009
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