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 A123168 Continued fraction for c = sqrt(2)*(exp(sqrt(2))-1)/(exp(sqrt(2))+1). 3
 0, 1, 6, 5, 14, 9, 22, 13, 30, 17, 38, 21, 46, 25, 54, 29, 62, 33, 70, 37, 78, 41, 86, 45, 94, 49, 102, 53, 110, 57, 118, 61, 126, 65, 134, 69, 142, 73, 150, 77, 158, 81, 166, 85, 174, 89, 182, 93, 190, 97, 198, 101, 206, 105, 214, 109, 222, 113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This continued fraction shows exp(sqrt(2)) is irrational. REFERENCES J. Borwein and D. Bailey, Mathematics by experiment, plausible reasoning in the 21st Century, A. K. Peters, p. 77 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1500 FORMULA a(2*n) = 4*n-3, a(2*n+1) = 8*n-2. From Colin Barker, Apr 15 2012: (Start) Conjecture: a(n) = 2*a(n-2) - a(n-4) for n>5. G.f.: x^2*(1+6*x+3*x^2+2*x^3)/((1-x)^2*(1+x)^2). (End) MATHEMATICA \$MinPrecision = 5 \$MachinePrecision; ContinuedFraction[Sqrt[2]* (Exp[Sqrt[2]] - 1)/(Exp[Sqrt[2]] + 1), 100]  (* G. C. Greubel, Aug 17 2018 *) PROG (PARI) default(realprecision, 1000); contfrac(sqrt(2)*(exp(sqrt(2))-1)/ (exp(sqrt(2))+1)) \\ Michel Marcus, Oct 11 2016 CROSSREFS Cf. A000217, A000384, A212343. Sequence in context: A309550 A274931 A120114 * A119636 A300750 A101493 Adjacent sequences:  A123165 A123166 A123167 * A123169 A123170 A123171 KEYWORD nonn,cofr AUTHOR Benoit Cloitre, Oct 02 2006 STATUS approved

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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)