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A097691 Denominators of the continued fraction n-1/(n-1/...) [n times]. 7
1, 2, 8, 56, 551, 6930, 105937, 1905632, 39424240, 922080050, 24057287759, 692686638072, 21817946138353, 746243766783074, 27543862067299424, 1091228270370045824, 46187969968474139807, 2080128468827570457762, 99318726126650358502921, 5011361251329169946919800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
LINKS
Pascual Jara and Miguel L. Rodríguez, Solving quadratic congruences, Arhimede Math. J. (2020) Vol. 7, No. 2, 105-120.
Eric Weisstein's World of Mathematics, Lucas Sequence
FORMULA
a(n) = ChebyshevU(n-1,n/2). - Gary Detlefs, Oct 15 2011
a(n) = abs((2^(-n) * (sqrt(4 - n^2) + i*n)^n - 2^n*(-sqrt(4 - n^2) - i*n)^(-n))/sqrt(4 - n^2)), where i is the imaginary unit, for n > 2. - Daniel Suteu, May 31 2017
a(n) ~ n^(n-1). - Vaclav Kotesovec, Jun 03 2017
EXAMPLE
a(4) = 56 because 4-1/(4-1/(4-1/4)) = 209/56.
MATHEMATICA
Table[s=n; Do[s=n-1/s, {n-1}]; Denominator[s], {n, 20}]
Table[Abs[Fibonacci[n, I n]], {n, 20}] (* Vladimir Reshetnikov, Oct 16 2018 *)
PROG
(Sage) [lucas_number1(n, n, 1) for n in range(1, 19)] # Zerinvary Lajos, Jul 16 2008
CROSSREFS
Cf. A084844, A084845, A097690 (numerators).
Sequence in context: A109618 A201128 A277498 * A181939 A124212 A326009
KEYWORD
easy,frac,nonn
AUTHOR
T. D. Noe, Aug 19 2004
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)