A113011 Decimal expansion of 1/(sqrt(e) - 1).

1, 5, 4, 1, 4, 9, 4, 0, 8, 2, 5, 3, 6, 7, 9, 8, 2, 8, 4, 1, 3, 1, 1, 0, 3, 4, 4, 4, 4, 7, 2, 5, 1, 4, 6, 3, 8, 3, 4, 0, 4, 5, 9, 2, 3, 6, 8, 4, 1, 8, 8, 2, 1, 0, 9, 4, 7, 4, 1, 3, 6, 9, 5, 6, 6, 3, 7, 5, 4, 2, 6, 3, 9, 1, 4, 3, 3, 1, 4, 8, 0, 7, 0, 7, 1, 8, 2, 5, 7, 2, 4, 0, 8, 5, 0, 0, 7, 7, 4, 2, 2, 4

Offset

1,2

Comments

Has continued fraction 1+2/(3+4/(5+6/7+...)).

Simple continued fraction is 1, 1, 1, 5, 1, 1, 9, 1, 1, 13, 1, 1, 17, 1, {1, 4k+1, 1}, ..., . - Robert G. Wilson v, Jul 01 2007

Links

G. C. Greubel, Table of n, a(n) for n = 1..20000

Leonhard Euler, On the formation of continued fractions, arXiv:math/0508227 [math.HO], 2005, see p. 14.

Michel Waldschmidt, Continued fractions, Ecole de recherche CIMPA-Oujda, Théorie des Nombres et ses Applications, 18 - 29 mai 2015: Oujda (Maroc).

Eric Weisstein's World of Mathematics, Continued Fraction.

Index entries for transcendental numbers

Formula

Equals Integral_{x = 0..oo} floor(2*x)*exp(-x) dx. - Peter Bala, Oct 09 2013

Equals 3/2 + Sum_{k>=0} tanh(1/2^(k+3))/2^(k+2). - Antonio Graciá Llorente, Jan 21 2024

Example

1.54149408253679828413110344447251463834045923684188210947413695663...

Mathematica

First@ RealDigits[ 1 / (Exp[1/2] - 1), 10, 111] (* Robert G. Wilson v, Jul 01 2007 *)
f[n_] := Fold[ Last@ #2 + First@ #2/#1 &, 2n - 1, Partition[ Reverse@ Range[ 2n - 2], 2]]; RealDigits[ f[61], 10, 105][[1]] (* Robert G. Wilson v, Jul 07 2012 *)

Prog

(PARI) 1/(sqrt(exp(1)) - 1) \\ G. C. Greubel, Apr 09 2018
(Magma) 1/(Sqrt(Exp(1)) - 1); // G. C. Greubel, Apr 09 2018

Crossrefs

Cf. A113012, A113013.

Sequence in context: A190287 A087707 A198352 * A028875 A130815 A342797

Adjacent sequences: A113008 A113009 A113010 * A113012 A113013 A113014

Keyword

nonn,cons

Author

Eric W. Weisstein, following a suggestion of Grover W. Hughes, Oct 09 2005

Extensions

Simpler definition from T. D. Noe, Oct 09 2005

Euler reference from David L. Harden, Oct 09 2005

Status

approved