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%I #6 Dec 17 2012 14:12:06
%S 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,
%T 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,
%U 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
%N Continued fraction expansion of the limit of a nested radical, sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... )))).
%C Sqrt(1 + Sqrt(2 + Sqrt(3 + Sqrt(4 + ... = 1.75793275661800...
%C Increasing partial continued fractions of the above are 1, 3, 7, 20, 115, 233, 301, 328, 16902, ...
%D Calvin C. Clawson, "Mathematical Mysteries, the beauty and magic of numbers," Perseus Books, Cambridge, Mass., 1996, pages 142 & 229.
%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, London, England, 1997, page 30.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NestedRadical.html">Nested Radical.</a>
%t ContinuedFraction[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 100]
%Y Cf. A072449.
%K cofr,nonn
%O 1,3
%A _Robert G. Wilson v_, Aug 01 2002
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