A226929 Values of n such that L(9) and N(9) 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, -65, 91, -227, 397, 471, -513, 555, -663, 663, 835, 861, -875, -1001, 1017, -1067, 1159, 1185, -1239, -1475, -1563, 1603, 1617, -1881, -1937, 1999, 2109, -2301, 2331, 2443, 2461, -2471, -2487, -2571, -2879, -2889, 2977, 2989, 3003, -3017, 3019, 3439, -3467, -3533, 3549, 3595, -3687, 3733, 3747, -3867, -3911, 3931, 4123, 4141, -4203, 4279, 4683, 4755, -4865, 4975, 4995

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 = 9; (* 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: A043021 A076287 A339997 * A212668 A020299 A250415

Adjacent sequences: A226926 A226927 A226928 * A226930 A226931 A226932

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Extensions

More terms from Vincenzo Librandi, Jul 13 2013

Status

approved