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 A097691 Denominators of the continued fraction n-1/(n-1/...) [n times]. 3

%I

%S 1,2,8,56,551,6930,105937,1905632,39424240,922080050,24057287759,

%T 692686638072,21817946138353,746243766783074,27543862067299424,

%U 1091228270370045824,46187969968474139807,2080128468827570457762,99318726126650358502921,5011361251329169946919800

%N Denominators of the continued fraction n-1/(n-1/...) [n times].

%C The (n-1)-th term of the Lucas sequence U(n,1). The numerator is the n-th term. Adjacent terms of the sequence U(n,1) are relatively prime.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LucasSequence.html">Lucas Sequence</a>

%F a(n) = ChebyshevU(n-1,n/2). [From Gary Detlefs, Oct 15 2011]

%e a(4) = 56 because 4-1/(4-1/(4-1/4)) = 209/56.

%t Table[s=n; Do[s=n-1/s, {n-1}]; Denominator[s], {n, 20}]

%o sage: [lucas_number1(n,n,1) for n in xrange(1,19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008

%Y Cf. A084844, A084845, A097690 (numerators).

%K easy,frac,nonn

%O 1,2

%A _T. D. Noe_, Aug 19 2004

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Last modified May 22 10:38 EDT 2013. Contains 225523 sequences.