A058292 Continued fraction for e^(Pi*sqrt(163)).

262537412640768743, 1, 1333462407511, 1, 8, 1, 1, 5, 1, 4, 1, 7, 1, 1, 1, 9, 1, 1, 2, 12, 4, 1, 15, 4, 299, 3, 5, 1, 4, 5, 5, 1, 28, 3, 1, 9, 4, 1, 6, 1, 1, 1, 1, 1, 1, 51, 11, 5, 3, 2, 1, 1, 1, 1, 2, 1, 5, 1, 9, 1, 2, 14, 1, 82, 1, 4, 1, 1, 1, 1, 1, 2, 3, 1, 1

Offset: 0

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• cofr
• nonn
• easy

Comments

The real number e^(pi*sqrt(163)) ~ a(0)+1-1/a(2) (cf also the Example section) is called Ramanujan's constant: See the main entry A060295 for further information. - M. F. Hasler, Jan 26 2014

Examples

			e^(Pi*Sqrt(163)) = 262537412640768743.99999999999925007259719818568887935385...
		

References

• Flajolet, Philippe, and Brigitte Vallée. "Continued fractions, comparison algorithms, and fine structure constants." Constructive, Experimental, and Nonlinear Analysis 27 (2000): 53-82. See Fig. 3.
• H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 179.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A060295, A019297.

Programs

Mathematica

ContinuedFraction[ E^(Pi*Sqrt[163]), 100 ]

PARI

default(realprecision,99);contfrac(exp(Pi*sqrt(163))) \\ With standard precision (38 digits), contfrac() returns only [a(0)+1]. - M. F. Hasler, Jan 26 2014