A058292 - OEIS

%I #12 Nov 21 2020 16:57:42

%S 262537412640768743,1,1333462407511,1,8,1,1,5,1,4,1,7,1,1,1,9,1,1,2,

%T 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,

%U 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

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

%C 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

%D 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.

%D H. M. Stark, An Introduction to Number Theory. Markham, Chicago, 1970, p. 179.

%H Ivan Panchenko, <a href="/A058292/b058292.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%o (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

%Y Cf. A060295, A019297.

%K cofr,nonn,easy

%O 0,1

%A _Robert G. Wilson v_, Dec 07 2000