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%I #34 Mar 21 2019 07:10:26
%S 1,3,-17,19,-39,39,-45,-65,73,-95,-101,129,-137,-153,165,207,-233,295,
%T -297,-323,339,-389,417,463,481,-521,-569,-597,-617,-687,729,753,-765,
%U 801,-855,-1005,-1025,1081,1093,-1115,1179,-1229,1231,-1235,-1245,-1275,-1287,1293,-1319,1345,-1389,1417,-1437,1495,-1521,1569,1749,1755,-1767,-1793,1807,1819,-1917
%N Values of n such that L(5) and N(5) 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, <a href="/A226925/b226925.txt">Table of n, a(n) for n = 1..295</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 = 5; (* 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 = 2000; 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 1,2
%A _N. J. A. Sloane_, Jul 12 2013
%E More terms from _Vincenzo Librandi_, Jul 13 2013
%E First term added from _Bruno Berselli_ at the suggestion of _Vincenzo Librandi_, Jul 15 2013
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