A072450 - OEIS

%I #10 Feb 16 2025 08:32:46

%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="https://mathworld.wolfram.com/NestedRadical.html">Nested Radical.</a>

%t ContinuedFraction[ Fold[ Sqrt[ #1 + #2] &, 0, Reverse[ Range[100]]], 100]

%Y Cf. A072449 (decimal expansion).

%K cofr,nonn

%O 0,3

%A _Robert G. Wilson v_, Aug 01 2002

%E Offset changed by _Andrew Howroyd_, Jul 06 2024