OFFSET
1,1
COMMENTS
The definition implies that k must be a prime.
The norm of (-1+sqrt(3))^k-1 is given by (-2)^k - lucasV(-2, -2, k)+1, where lucasV(-2, -2, k) is the solution of the recurrence relation v(n) = -2*v(n-1) + 2*v(n-2) with v(0)=2 and v(1)=-2.
a(29) > 517000. - Serge Batalov, Oct 24 2024
LINKS
Mike Oakes, Posting to primenumbers list on Feb 08 2002
Mike Oakes, 4 new forms of primes, digest of 4 messages in primenumbers Yahoo group, Feb 8 - Feb 11, 2002.
EXAMPLE
3 is a term because (-2)^3-lucasV(-2,-2,3)+1 = -8-(-20)+1 = 13 and 13 is prime.
MATHEMATICA
v[0] = 2; v[1] = -2; v[n_] := v[n] = -2*v[n-1] + 2*v[n-2] ; s = {}; Do[If[PrimeQ[(-2)^n - v[n] + 1], Print[n]; AppendTo[s, n]], {n, 8171}]; s (* Jean-François Alcover, Apr 18 2011 *)
PROG
(PARI) isok(n)={ispseudoprime(([0, 1; 2, 2]^n*[2; 2])[1, 1] - 2^n - (-1)^n)} \\ Andrew Howroyd, Oct 24 2024
CROSSREFS
KEYWORD
nonn,nice,more
AUTHOR
Mike Oakes, Feb 09 2002
EXTENSIONS
Corrected and extended by Aurelien Gibier, Oct 24 2024
a(28) from Serge Batalov, Oct 24 2024
STATUS
approved