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Values of n such that L(8) and N(8) 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 #26 Mar 21 2019 07:10:49

%S -179,-209,-263,-395,547,841,-1373,-1535,2101,2143,2161,2245,-2285,

%T 2761,2911,-2927,-3125,3175,-3539,-3593,3625,-3779,3805,-4175,4255,

%U -4469,-4493,4495,4507,4567,4603,-4937,-5009,-5333,5737,6037,-6215,-6479,-6575,6763,-6803,6847,-6947,-7925,8077,-8129,-8285,-8543,8797

%N Values of n such that L(8) and N(8) 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="/A226928/b226928.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 = 8; (* 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 = 9000; 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