Search: id:A107920
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%I A107920
%S A107920 0,1,1,1,3,1,5,7,3,17,11,23,45,1,91,89,93,271,85,457,627,287,1541,967,
%T A107920 2115,4049,181,8279,7917,8641,24475,7193,41757,56143,27371,139657,84915,
%U A107920 194399,364229,24569,753027,703889,802165,2209943,605613,3814273
%V A107920 0,1,1,-1,-3,-1,5,7,-3,-17,-11,23,45,-1,-91,-89,93,271,85,-457,-627,287,
               1541,967,-2115,
%W A107920 -4049,181,8279,7917,-8641,-24475,-7193,41757,56143,-27371,-139657,-84915,
               194399,
%X A107920 364229,-24569,-753027,-703889,802165,2209943,605613,-3814273
%N A107920 Lucas and Lehmer numbers with parameters (1+-sqrt(-7))/2.
%C A107920 This is an example of a sequence of Lehmer numbers. In this case, the 
               two parameters, alpha and beta, are (1 +- i Sqrt(7))/2. Bilu, Hanrot, 
               Voutier and Mignotte show that all terms of a Lehmer sequence a(n) 
               have a primitive factor for n > 30. Note that for this sequence, 
               a(30) = 24475 = 5*5*11*89 has no primitive factors. - T. D. Noe (noe(AT)sspectra.com), 
               Oct 29 2003
%C A107920 Row sums of Riordan array (1/(1+2x^2),x/(1+2x^2)). - Paul Barry (pbarry(AT)wit.ie), 
               Sep 10 2005
%H A107920 Y. Bilu, G. Hanrot, P. M. Voutier and M. Mignotte, <a href="http://www.inria.fr/
               rrrt/rr-3792.html">Existence of primitive divisors of Lucas and Lehmer 
               numbers</a>
%H A107920 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LehmerNumber.html">Lehmer Number</a>
%F A107920 G.f.; x/(1-x+2x^2). a(n)=a(n-1)-2*a(n-2).
%F A107920 a(n+1)=sum{k=0..n, C((n+k)/2, k)*(-2)^((n-k)/2)*(1+(-1)^(n-k))/2}; a(n+1)=sum{k=0..floor(n/
               2), C(n-k, k)(-2)^k}; - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005
%F A107920 a(n+1)=Sum_{k, 0<=k<=n} A109466(n,k)*2^(n-k). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 26 2008]
%p A107920 a:= n-> (Matrix([[1,1],[ -2,0]])^n)[1,2]: seq (a(n), n=0..45); [From 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2008]
%o A107920 (PARI) a(n)=if(n<0,0,imag(quadgen(-7)^n))
%o A107920 (Other) sage: [lucas_number1(n,1,+2) for n in xrange(0, 46)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A107920 A001607(n)=-(-1)^n*a(n).
%Y A107920 Sequence in context: A001607 A167433 A077020 this_sequence A159285 A021080 
               A049764
%Y A107920 Adjacent sequences: A107917 A107918 A107919 this_sequence A107921 A107922 
               A107923
%K A107920 sign
%O A107920 0,5
%A A107920 Michael Somos, May 28 2005

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