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Search: id:A097691
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| A097691 |
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Denominators of the continued fraction n-1/(n-1/...) [n times]. |
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+0
4
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| 1, 2, 8, 56, 551, 6930, 105937, 1905632, 39424240, 922080050, 24057287759, 692686638072, 21817946138353, 746243766783074, 27543862067299424, 1091228270370045824, 46187969968474139807, 2080128468827570457762
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Lucas Sequence
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EXAMPLE
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a(4)=56 because 4-1/(4-1/(4-1/4))=209/56
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MATHEMATICA
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Table[s=n; Do[s=n-1/s, {n-1}]; Denominator[s], {n, 20}]
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PROGRAM
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sage: [lucas_number1(n, n, 1) for n in xrange(1, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
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CROSSREFS
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Cf. A084844, A084845, A097690 (numerators).
Sequence in context: A073831 A009298 A113248 this_sequence A124212 A005439 A128814
Adjacent sequences: A097688 A097689 A097690 this_sequence A097692 A097693 A097694
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KEYWORD
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easy,frac,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Aug 19 2004
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