A226927 Values of n such that L(7) and N(7) 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.

9, -15, -95, 109, -243, -297, 297, 457, 459, -477, 583, 723, -761, -771, -983, 1045, 1047, 1077, 1287, 1305, -1373, 1389, -1481, -2063, -2073, 2085, 2173, -2223, 2263, -2367, 2503, -2591, -2615, -2643, 2643, 2755, -2955, -2957, 2995, 3105, -3153, 3153, 3237, 3243, -3267, -3491, 3667, 3699, 3847, 3919, -4023, -4217, 4255, -4275, 4377, 4483, 4549, 4743, 4827, 4855, -4973

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 = 7; (* 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 = 5000; 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: A100663 A304457 A219129 * A152219 A173037 A029712

Adjacent sequences: A226924 A226925 A226926 * A226928 A226929 A226930

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Extensions

More terms from Vincenzo Librandi, Jul 13 2013

Status

approved