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Search: id:A072450
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| A072450 |
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Continued fraction expansion of the limit of a nested radical, sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... )))). |
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2
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| 1, 1, 3, 7, 1, 1, 1, 2, 3, 1, 4, 1, 1, 2, 1, 2, 20, 1, 2, 2, 2, 1, 2, 1, 1, 6, 2, 8, 5, 13, 2, 3, 1, 1, 115, 1, 4, 38, 4, 3, 1, 2, 1, 1, 1, 14, 1, 10, 4, 4, 5, 2, 2, 3, 19, 1, 1, 1, 5, 2, 1, 4, 1, 3, 1, 3, 4, 1, 8, 47, 33, 1, 1, 5, 13, 1, 14, 1, 5, 1, 1, 2, 17, 2, 1, 108, 9, 16, 3, 1, 2, 2, 3, 1, 5, 6, 2
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Sqrt(1 + Sqrt(2 + Sqrt(3 + Sqrt(4 + ... = 1.75793275661800...
Increasing partial continued fractions of the above are 1, 3, 7, 20, 115, 233, 301, 328, 16902, ...
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REFERENCES
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Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, London, England, 1997, page 30.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
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MATHEMATICA
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ContinuedFraction[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 100]
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CROSSREFS
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Cf. A072449.
Sequence in context: A103844 A074051 A048292 this_sequence A085785 A127929 A003118
Adjacent sequences: A072447 A072448 A072449 this_sequence A072451 A072452 A072453
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KEYWORD
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cofr,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 01 2002
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