A226928 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.

-179, -209, -263, -395, 547, 841, -1373, -1535, 2101, 2143, 2161, 2245, -2285, 2761, 2911, -2927, -3125, 3175, -3539, -3593, 3625, -3779, 3805, -4175, 4255, -4469, -4493, 4495, 4507, 4567, 4603, -4937, -5009, -5333, 5737, 6037, -6215, -6479, -6575, 6763, -6803, 6847, -6947, -7925, 8077, -8129, -8285, -8543, 8797

Offset

1,1

Comments

Computed with PARI using commands similar to those used to compute A226921.

Links

Vincenzo Librandi and Joerg Arndt, Table of n, a(n) for n = 1..1000

Eric L. F. Roettger, A cubic extension of the Lucas functions, Thesis, Dept. of Mathematics and Statistics, Univ. of Calgary, 2009. See page 195.

Mathematica

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 *)

Crossrefs

Cf. A226921-A226929, A227448, A227449, A227515-A227523.

Sequence in context: A140026 A108384 A217550 * A162164 A238893 A230809

Adjacent sequences: A226925 A226926 A226927 * A226929 A226930 A226931

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Status

approved