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A226922 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. 1

%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] (* _Jean-Fran├žois 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 1,3

%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

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)