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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188739 Decimal expansion of e+sqrt(e^2-1). 7
5, 2, 4, 5, 9, 4, 0, 0, 5, 2, 7, 7, 0, 7, 5, 9, 8, 5, 6, 4, 6, 1, 1, 4, 6, 6, 8, 6, 1, 6, 3, 7, 6, 9, 7, 2, 6, 8, 5, 1, 4, 7, 1, 9, 8, 5, 3, 0, 1, 5, 6, 2, 6, 8, 8, 1, 9, 8, 6, 6, 1, 8, 7, 8, 6, 3, 8, 4, 4, 4, 1, 7, 2, 2, 5, 7, 8, 7, 4, 0, 4, 7, 3, 8, 9, 8, 7, 2, 8, 5, 0, 0, 5, 9, 2, 9, 5, 7, 5, 5, 1, 9, 9, 5, 0, 0, 2, 5, 9, 8, 6, 8, 4, 2, 4, 1, 3, 5, 0, 8, 4, 0, 4, 2, 1, 9, 7, 2, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Decimal expansion of the shape of a greater 2e-contraction rectangle; see A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and the partitioning of these rectangles into sets of squares in a manner that matches the continued fractions of their shapes.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

e+sqrt(-1+e^2), with continued fraction A188627.

EXAMPLE

5.24594005277075985646114668616376972685147198530... = 1/A188738 .

MATHEMATICA

r = 2 E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]] (* A188739 *)

ContinuedFraction[t, 120] (* A188627 *)

PROG

(PARI) default(realprecision, 100); exp(1) + sqrt(exp(2) - 1) \\ G. C. Greubel, Nov 01 2018

(MAGMA) SetDefaultRealField(RealField(100)); Exp(1) + Sqrt(Exp(2) -1); // G. C. Greubel, Nov 01 2018

CROSSREFS

Cf. A188738 (inverse), A188627 (continued fraction).

Sequence in context: A266122 A064853 A177148 * A265287 A257701 A202494

Adjacent sequences:  A188736 A188737 A188738 * A188740 A188741 A188742

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Apr 11 2011

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 11:32 EST 2018. Contains 318086 sequences. (Running on oeis4.)