A160327 Decimal expansion of (e-1)/(e+1).

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

Offset: 0

Author

Harry J. Smith, May 09 2009

Keywords

• nonn
• easy
• cons

Examples

			0.462117157260009758502318483643672548730289280330113038552731815838080...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Index entries for transcendental numbers

Crossrefs

Cf. A016825 (continued fraction), A086403/A079165 (convergents).

Cf. A000367, A002445.

Programs

Magma

SetDefaultRealField(RealField(100)); (Exp(1) - 1)/(Exp(1) + 1); // G. C. Greubel, Oct 05 2018

Mathematica

RealDigits[(E-1)/(E+1), 10, 100][[1]] (* G. C. Greubel, Oct 05 2018 *)

PARI

default(realprecision, 20080); x=tanh(1/2)*10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b160327.txt", n, " ", d));

PARI

(exp(1)-1)/(exp(1)+1) \\ Altug Alkan, Oct 05 2018

Formula

(e-1)/(e+1) = tanh(1/2).

Equals 2 * Sum_{k>=1} (2^(2*k)-1)*B(2*k)/(2*k)!, where B(2*k) = A000367(k)/A002445(k) are the Bernoulli numbers. - Amiram Eldar, Nov 25 2020

Equals -i * tan(i/2). - Michal Paulovic, Jan 03 2023