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%I #21 Mar 21 2019 04:29:18
%S -3,7,19,25,-33,39,-51,-65,79,105,117,177,-231,259,-401,483,499,-513,
%T 529,-597,-635,-705,723,-747,-861,-863,-887,-905,-933,-1017,1033,1089,
%U -1125,-1155,-1235,-1307,1425,-1461,-1473,1579,1635,1687,1719,-1785,1797,1839,1965,-2051,-2093,2137,-2201,2217,-2331,-2385,2445,2485,2587,-2597,2599,-2607,-2625,-2781,2839,2907
%N Values of n such that L(3) and N(3) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.
%H Vincenzo Librandi and Joerg Arndt, <a href="/A226923/b226923.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric L. F. Roettger, <a href="http://people.ucalgary.ca/~hwilliam/files/A_Cubic_Extention_of_the_Lucas_Functions.pdf">A cubic extension of the Lucas functions</a>, Thesis, Dept. of Mathematics and Statistics, Univ. of Calgary, 2009. See page 195.
%t k = 3; (* adjust for related sequences *) fL[n_] := (n^2 + n + 1)*2^(2*k) + (2*n + 1)*2^k + 1; fN[n_] := (n^2 + n + 1)*2^k + n; nn = 3000; A = {}; For[n = -nn, n <= nn, n++, If[PrimeQ[fL[n]] && PrimeQ[fN[n]], AppendTo[A, n]]]; cmpfunc[x_, y_] := If[x == y, Return[True], ax = Abs[x]; ay = Abs[y]; If[ax == ay, Return[x < y], Return[ ax < ay]]]; Sort[A, cmpfunc] (* _Jean-François Alcover_, Jul 17 2013, translated and adapted from Joerg Arndt's Pari program in A226921 *)
%Y Cf. A226921-A226929, A227448, A227449, A227515-A227523.
%K sign
%O 1,1
%A _N. J. A. Sloane_, Jul 12 2013
%E More terms from _Vincenzo Librandi_, Jul 13 2013
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