A194807 Decimal expansion of 1/(e-2).

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

Offset

1,2

Comments

The value of the continued fraction 1+1/(2+2/(3+3/(4+4/(5+5/(6+6/(...)))))).

Links

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

Index entries for transcendental numbers

Formula

Define s(n) = Sum_{k = 2..n} 1/k! for n >= 2. Then 1/(e - 2) = 2! - Sum_ {n >= 2} 1/( (n+1)!*s(n)*s(n+1) ) is a rapidly converging series of rationals. Cf. A073333. Equivalently, 1/(e - 2) = 2! - 2!/(1*4) - 3!/(4*17) - 4!/(17*86) - ..., where [1, 4, 17, 86, ... ] is A056542. Cf. A002627 and A185108. - Peter Bala, Oct 09 2013

Example

1.392211191177332814376552878479816528373978385315...

Mathematica

RealDigits[1/(E - 2), 10, 105][[1]] (* T. D. Noe, May 07 2012 *)
Fold[Function[#2 + #2/#1], 1, Reverse[Range[100]]] // N[#, 105]& // RealDigits // First (* Jean-François Alcover, Sep 19 2014 *)

Prog

(PARI)
default(realprecision, 110);
1/(exp(1)-2)
\\ Joerg Arndt, May 07 2012
(Magma) 1/(Exp(1) - 2); // G. C. Greubel, Apr 09 2018

Crossrefs

Cf. A073333 (1/(e-1)), A002627, A185108.

Sequence in context: A256501 A229099 A021259 * A114875 A275371 A225357

Adjacent sequences: A194804 A194805 A194806 * A194808 A194809 A194810

Keyword

cons,easy,nonn

Author

Martin Janecke, May 06 2012

Status

approved