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A058292
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Continued fraction for e^(Pi*sqrt(163)).
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4
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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EXAMPLE
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e^(Pi*Sqrt(163)) = 262537412640768743.99999999999925007259719818568887935385...
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MATHEMATICA
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ContinuedFraction[ E^(Pi*Sqrt[163]), 100 ]
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PROG
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(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
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CROSSREFS
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KEYWORD
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cofr,nonn,easy
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AUTHOR
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STATUS
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approved
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