OFFSET
0,3
COMMENTS
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, ...
REFERENCES
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.
LINKS
Eric Weisstein's World of Mathematics, Nested Radical.
MATHEMATICA
ContinuedFraction[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 100]
CROSSREFS
KEYWORD
cofr,nonn
AUTHOR
Robert G. Wilson v, Aug 01 2002
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 06 2024
STATUS
approved