A226921 Values of n such that L(1) and N(1) 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.

0, 1, -3, 3, -5, 13, 25, 31, -33, 37, -39, 55, -57, -71, 79, -87, -159, 181, -183, 219, -221, -243, -255, 255, 279, -281, 289, -291, 307, 325, 333, -353, -369, 375, -395, -423, -435, -495, -501, 507, -551, -579, -633, 703, -711, -731, 739, 781, 825, -857, 891, 907, 927, 955, -957, -963, -981

Offset

1,3

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 = 1; (* 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 = 1000; 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 *)

Prog

(PARI)
k=1;  /* 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;
N=1000;  A=[];
for(n=-N, +N, if (isprime(fL(n)) & isprime(fN(n)), A=concat(A, n) ) );
cmpfunc(x, y)= {
    if(x==y, return(0) );
    my( ax=abs(x), ay=abs(y) );
    if ( ax==ay, return( sign(x-y) ) );
    return( sign(ax-ay) );
}
A=vecsort(A, cmpfunc)
\\ Joerg Arndt, Jul 15 2013

Crossrefs

Cf. A226921-A226929, A227448, A227449, A227515-A227523.

Sequence in context: A144419 A212322 A367005 * A133190 A052898 A183483

Adjacent sequences: A226918 A226919 A226920 * A226922 A226923 A226924

Keyword

sign

Author

N. J. A. Sloane, Jul 12 2013

Extensions

More terms from Vincenzo Librandi, Jul 15 2013

Status

approved