A309419 Decimal expansion of e/(e-2).

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

Offset

1,1

Comments

This can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":

1

e/(e-2) = 4 - --------------------

2

5 - ----------------

3

6 - ------------

4

7 - --------

8 - ... .

For a proof by humans see the arXiv:1907.00205 preprint linked below.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Gal Raayoni, George Pisha, Yahel Manor, Uri Mendlovic, Doron Haviv, Yaron Hadad, and Ido Kaminer, The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants, arXiv:1907.00205 [cs.LG], 2019-2020.

The Ramanujan Machine, Using algorithms to discover new mathematics.

Formula

Equals 1/A334397.

Example

3.78442238235466562875310575695963305674795677063...

Maple

nn:= 126: # number of digits
b:= i-> `if`(i<nn, i+3 -i/b(i+1), 1):
evalf(b(1), nn);

Mathematica

RealDigits[E/(E-2), 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)

Crossrefs

Cf. A001113, A309091, A309420, A334397.

Sequence in context: A267501 A016667 A006834 * A064540 A303276 A264826

Adjacent sequences: A309416 A309417 A309418 * A309420 A309421 A309422

Keyword

nonn,cons

Author

Alois P. Heinz, Jul 30 2019

Status

approved