A309419 - OEIS

%I #26 Jun 28 2023 08:21:49

%S 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,

%T 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,

%U 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

%N Decimal expansion of e/(e-2).

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

%C                              1

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

%C                                2

%C                     5 - ----------------

%C                                  3

%C                         6 - ------------

%C                                    4

%C                             7 - --------

%C                                  8 - ...  .

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

%H Alois P. Heinz, <a href="/A309419/b309419.txt">Table of n, a(n) for n = 1..10000</a>

%H Gal Raayoni, George Pisha, Yahel Manor, Uri Mendlovic, Doron Haviv, Yaron Hadad, and Ido Kaminer, <a href="https://arxiv.org/abs/1907.00205">The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants</a>, arXiv:1907.00205 [cs.LG], 2019-2020.

%H The Ramanujan Machine, <a href="http://www.ramanujanmachine.com/">Using algorithms to discover new mathematics</a>.

%F Equals 1/A334397.

%e 3.78442238235466562875310575695963305674795677063...

%p nn:= 126: # number of digits

%p b:= i-> `if`(i<nn, i+3 -i/b(i+1), 1):

%p evalf(b(1), nn);

%t RealDigits[E/(E-2), 10, 120][[1]] (* _Amiram Eldar_, Jun 28 2023 *)

%Y Cf. A001113, A309091, A309420, A334397.

%K nonn,cons

%O 1,1

%A _Alois P. Heinz_, Jul 30 2019