login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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