

A067834


Norm in ring Z[sqrt(3)] of (((1+sqrt(3))^n)1) is prime


0



2, 3, 7, 13, 19, 43, 61, 151, 257, 751, 859, 1453, 3767, 3889, 8171, 15959, 61961
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..17.
M. Oakes, Posting to primenumbers list on Feb 08 2002


FORMULA

(2)^nlucasV(2, 2, n)+1, where lucasV(2, 2, n) is the solution of the recurrence relation v[0]=2, v[1]=2, v[n+2]=2*v[n+1]+2*v[n] n >= 0.


EXAMPLE

a(2)=3 because (2)^3lucasV(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[n1] + 2*v[n2] ; s = {}; Do[If[PrimeQ[(2)^n  v[n] + 1], Print[n]; AppendTo[s, n]], {n, 8171}]; s (* JeanFrançois Alcover, Apr 18 2011 *)


CROSSREFS

Sequence in context: A019383 A171817 A156300 * A070754 A049887 A048216
Adjacent sequences: A067831 A067832 A067833 * A067835 A067836 A067837


KEYWORD

easy,nice,nonn


AUTHOR

Mike Oakes, Feb 09 2002


STATUS

approved



