The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A202540

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A202540

Decimal expansion of the number x satisfying e^(3x)-e^(-x)=1.
(history; published version)

#11 by Charles R Greathouse IV at Tue May 14 23:54:54 EDT 2019

STATUS

editing

approved

#10 by Charles R Greathouse IV at Tue May 14 23:54:52 EDT 2019

LINKS

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

EXAMPLE

x=0.19946057824300535148857771838494917839277692...

PROG

(PARI) log(polrootsreal(x^4-x-1)[2]) \\ Charles R Greathouse IV, May 14 2019

STATUS

approved

editing

#9 by Bruno Berselli at Wed Feb 27 05:20:36 EST 2013

STATUS

editing

approved

#8 by Bruno Berselli at Wed Feb 27 05:20:02 EST 2013

NAME

Decimal expansion of the number x satisfying e^(3x)-e^(-x)=1.

COMMENTS

See A202537 for a guide to related sequences. The Mathematica program includes a graph.

STATUS

proposed

editing

#7 by Jean-François Alcover at Wed Feb 27 04:59:37 EST 2013

STATUS

editing

proposed

#6 by Jean-François Alcover at Wed Feb 27 04:59:31 EST 2013

MATHEMATICA

RealDigits[ Log[ Root[#^4 - # - 1&, 2]], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:58:03 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 21 2011

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/285

#4 by N. J. A. Sloane at Wed Dec 21 18:15:07 EST 2011

STATUS

proposed

approved

#3 by Clark Kimberling at Wed Dec 21 17:48:58 EST 2011

STATUS

editing

proposed

#2 by Clark Kimberling at Wed Dec 21 12:02:07 EST 2011

NAME

allocated for Clark KimberlingDecimal expansion of the number x satisfying e^3x-e^(-x)=1.

DATA

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

OFFSET

0,2

COMMENTS

See A202537 for a guide to related sequences. The Mathematica program includes a graph.

EXAMPLE

x=0.19946057824300535148857771838494917839277692...

MATHEMATICA

u = 3; v = 1;

f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1

Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]

RealDigits[r] (* A202540 *)

CROSSREFS

Cf. A202537.

KEYWORD

allocated

nonn,cons

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Dec 21 2011

STATUS

approved

editing