A226923 Values of n such that L(3) and N(3) 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.

-3, 7, 19, 25, -33, 39, -51, -65, 79, 105, 117, 177, -231, 259, -401, 483, 499, -513, 529, -597, -635, -705, 723, -747, -861, -863, -887, -905, -933, -1017, 1033, 1089, -1125, -1155, -1235, -1307, 1425, -1461, -1473, 1579, 1635, 1687, 1719, -1785, 1797, 1839, 1965, -2051, -2093, 2137, -2201, 2217, -2331, -2385, 2445, 2485, 2587, -2597, 2599, -2607, -2625, -2781, 2839, 2907

Offset

1,1

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 = 3; (* 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 = 3000; 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: A127925 A032388 A050866 * A001985 A203321 A203319

Adjacent sequences: A226920 A226921 A226922 * A226924 A226925 A226926

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Extensions

More terms from Vincenzo Librandi, Jul 13 2013

Status

approved