A226926 - OEIS

A226926

Values of n such that L(6) and N(6) 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.

-65, 145, 259, -311, -635, 679, -1001, 1099, -1109, -1475, 1549, -1571, 1885, 1969, -1991, 2125, -2165, 2191, 2431, -3005, -3269, 3451, -3719, -3941, -4265, 4975, 5359, 5731, -5861, 6109, -6221, -6359, 6409, 6529, -6695, -6851, 7105, 7525, 7681, 7879, -8165, 8365, -8711, 9109, -9221, -9299, -9305, 9349, -9761, 9835, 9919

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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 = 6; (* 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 = 10000; 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: A092226 A211255 A297849 * A345700 A121944 A044316

Adjacent sequences: A226923 A226924 A226925 * A226927 A226928 A226929

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Jul 12 2013

EXTENSIONS

More terms from Vincenzo Librandi, Jul 13 2013

STATUS

approved