A072450 Continued fraction expansion of the limit of a nested radical, sqrt(1 + sqrt(2 + sqrt(3 + sqrt(4 + ... )))).

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

Offset

1,3

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

Table of n, a(n) for n=1..97.

Eric Weisstein's World of Mathematics, Nested Radical.

Mathematica

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

Crossrefs

Cf. A072449.

Sequence in context: A074051 A335918 A048292 * A085785 A200235 A127929

Adjacent sequences: A072447 A072448 A072449 * A072451 A072452 A072453

Keyword

cofr,nonn

Author

Robert G. Wilson v, Aug 01 2002

Status

approved