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A067834
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Norm in ring Z[sqrt(3)] of (((-1+sqrt(3))^n)-1) is prime
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0
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2, 3, 7, 13, 19, 43, 61, 151, 257, 751, 859, 1453, 3767, 3889, 8171, 15959, 61961
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| M. Oakes, Posting to primenumbers list on Feb 08 2002
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FORMULA
| (-2)^n-lucasV(-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.
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EXAMPLE
| a(2)=3 because (-2)^3-lucasV(-2,-2,3)+1 = -8-(-20)+1 = 13 and 13 is prime.
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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 (* From Jean-François Alcover, Apr 18 2011 *)
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CROSSREFS
| Sequence in context: A019383 A171817 A156300 * A070754 A049887 A048216
Adjacent sequences: A067831 A067832 A067833 * A067835 A067836 A067837
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Mike Oakes (mikeoakes2(AT)aol.com), Feb 09 2002
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