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Search: id:A097690
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| A097690 |
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Numerators of the continued fraction n-1/(n-1/...) [n times]. |
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+0
4
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| 1, 3, 21, 209, 2640, 40391, 726103, 15003009, 350382231, 9127651499, 262424759520, 8254109243953, 281944946167261, 10393834843080975, 411313439034311505, 17391182043967249409, 782469083251377707328
(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-th term of the Lucas sequence U(n,1). The denominator is the (n-1)-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)=209 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}]; Numerator[s], {n, 20}]
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PROGRAM
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sage: [lucas_number1(n, n-1, 1) for n in range(19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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Cf. A084844, A084845, A097691 (denominators).
Adjacent sequences: A097687 A097688 A097689 this_sequence A097691 A097692 A097693
Sequence in context: A132863 A136223 A114469 this_sequence A037967 A123691 A087918
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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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