|
| |
|
|
A097691
|
|
Denominators of the continued fraction n-1/(n-1/...) [n times].
|
|
3
| |
|
|
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; 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
| Eric Weisstein's World of Mathematics, Lucas Sequence
|
|
|
FORMULA
| a(n) = ChebyshevU(n-1,n/2). [From Gary Detlefs, Oct 15 2011]
|
|
|
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}]
|
|
|
PROG
| sage: [lucas_number1(n, n, 1) for n in xrange(1, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
|
|
|
CROSSREFS
| Cf. A084844, A084845, A097690 (numerators).
Sequence in context: A113248 A109618 A201128 * A124212 A197949 A005439
Adjacent sequences: A097688 A097689 A097690 * A097692 A097693 A097694
|
|
|
KEYWORD
| easy,frac,nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Aug 19 2004
|
| |
|
|
