A227519 Values of n such that L(16) and N(16) 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.

-89, 277, -389, -395, -407, -785, -1025, 1231, 1327, -1433, 1501, -1919, -2783, -2825, 2881, -2915, 2935, 3097, 3247, -3623, -3995, -4397, 4903, 5053, 5071, 5113, -5555, -5639, 5683, -5783, -6497, 6583, -7109, -7295, -7355, 7867, -7883, -8825, -9059, 9643, -9719, -9857, -10973

Offset

1,1

Comments

Computed with PARI using commands similar to those used to compute A226921.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..268

Eric L. F. Roettger, A cubic extension of the Lucas functions, Thesis, Dept. of Mathematics and Statistics, Univ. of Calgary, 2009. See page 195.

Prog

(PARI)
L(n, k)={(n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1};
N(n, k)={(n^2+n+1)*2^k + n}
ok(n)={isprime(L(n, 16))&&isprime(N(n, 16))}
seq(n)={my(list=List()); my(k=1); while(#list<n, if(ok(k), listput(list, k)); k=-k+(k<0)); Vec(list)}
seq(60) \\ Andrew Howroyd, Feb 23 2018

Crossrefs

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

Sequence in context: A008900 A238681 A320909 * A142393 A142045 A142936

Adjacent sequences: A227516 A227517 A227518 * A227520 A227521 A227522

Keyword

sign,easy

Author

Vincenzo Librandi, Jul 14 2013

Extensions

a(250) in b-file corrected by Andrew Howroyd, Feb 23 2018

Status

approved