%I
%S 1,1,11,31,55,115,191,221,271,361,515,601,641,695,745,1061,
%T 1075,1201,1259,1399,1495,1651,1669,1915,2381,2449,2921,2959,2969,
%U 2971,3035,3049,3215,3265,3419,3611,3709,3889,4045,4229,4241,4301,4561,4565,4589,4721,4849,4931,5039,5081,5555,5795,5821,5879,5921
%N Values of n such that L(2) and N(2) 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.
%C Computed with PARI using commands similar to those used to compute A226921.
%H Vincenzo Librandi and Joerg Arndt, <a href="/A226922/b226922.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 = 2; (* 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 = 6000; 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] (* _JeanFrançois Alcover_, Jul 17 2013, translated and adapted from Joerg Arndt's Pari program in A226921 *)
%Y Cf. A226921A226929, A227448, A227449, A227515A227523.
%K sign
%O 1,3
%A _N. J. A. Sloane_, Jul 12 2013
%E More terms from _Vincenzo Librandi_, Jul 13 2013
%E First two terms added from _Bruno Berselli_, at the suggestion of _Vincenzo Librandi_, Jul 15 2013
