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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 July 8 00:40 EDT 2020. Contains 335502 sequences. (Running on oeis4.)