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%I #20 Mar 21 2023 09:18:12
%S 2,3,7,13,19,43,61,151,257,751,859,1453,3767,3889,8171,15959,61961
%N Norm in ring Z[sqrt(3)] of (((-1+sqrt(3))^n)-1) is prime.
%H Mike Oakes, <a href="http://groups.yahoo.com/group/primenumbers/message/5217">Posting to primenumbers list on Feb 08 2002</a>
%H Mike Oakes, <a href="/A067834/a067834.txt">4 new forms of primes</a>, digest of 4 messages in primenumbers Yahoo group, Feb 8 - Feb 11, 2002.
%F (-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.
%e a(2)=3 because (-2)^3-lucasV(-2,-2,3)+1 = -8-(-20)+1 = 13 and 13 is prime.
%t 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 *)
%K nonn,nice,more
%O 1,1
%A _Mike Oakes_, Feb 09 2002
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