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, 1, -11, 31, 55, 115, -191, -221, 271, 361, -515, 601, -641, -695, 745, -1061, 1075, 1201, -1259, 1399, 1495, 1651, 1669, 1915, -2381, 2449, -2921, 2959, -2969, 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

Offset

1,3

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 = 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-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: A057630 A057628 A144364 * A031372 A028877 A087394

Adjacent sequences: A226919 A226920 A226921 * A226923 A226924 A226925

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Extensions

More terms from Vincenzo Librandi, Jul 13 2013

First two terms added from Bruno Berselli, at the suggestion of Vincenzo Librandi, Jul 15 2013

Status

approved