

A226925


Values of n such that L(5) and N(5) 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, 3, 17, 19, 39, 39, 45, 65, 73, 95, 101, 129, 137, 153, 165, 207, 233, 295, 297, 323, 339, 389, 417, 463, 481, 521, 569, 597, 617, 687, 729, 753, 765, 801, 855, 1005, 1025, 1081, 1093, 1115, 1179, 1229, 1231, 1235, 1245, 1275, 1287, 1293, 1319, 1345, 1389, 1417, 1437, 1495, 1521, 1569, 1749, 1755, 1767, 1793, 1807, 1819, 1917
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..295
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 = 5; (* 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 = 2000; 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] (* JeanFrançois 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: A019342 A029473 A103088 * A259772 A082387 A032923
Adjacent sequences: A226922 A226923 A226924 * A226926 A226927 A226928


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Jul 12 2013


EXTENSIONS

More terms from Vincenzo Librandi, Jul 13 2013
First term added from Bruno Berselli at the suggestion of Vincenzo Librandi, Jul 15 2013


STATUS

approved



