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

%I A309419 #26 Jun 28 2023 08:21:49
%S A309419 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 A309419 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 A309419 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 A309419 Decimal expansion of e/(e-2).
%C A309419 This can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":
%C A309419                              1
%C A309419     e/(e-2)  =  4 - --------------------
%C A309419                                2
%C A309419                     5 - ----------------
%C A309419                                  3
%C A309419                         6 - ------------
%C A309419                                    4
%C A309419                             7 - --------
%C A309419                                  8 - ...  .
%C A309419   For a proof by humans see the arXiv:1907.00205 preprint linked below.
%H A309419 Alois P. Heinz, <a href="/A309419/b309419.txt">Table of n, a(n) for n = 1..10000</a>
%H A309419 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 A309419 The Ramanujan Machine, <a href="http://www.ramanujanmachine.com/">Using algorithms to discover new mathematics</a>.
%F A309419 Equals 1/A334397.
%e A309419 3.78442238235466562875310575695963305674795677063...
%p A309419 nn:= 126: # number of digits
%p A309419 b:= i-> `if`(i<nn, i+3 -i/b(i+1), 1):
%p A309419 evalf(b(1), nn);
%t A309419 RealDigits[E/(E-2), 10, 120][[1]] (* _Amiram Eldar_, Jun 28 2023 *)
%Y A309419 Cf. A001113, A309091, A309420, A334397.
%K A309419 nonn,cons
%O A309419 1,1
%A A309419 _Alois P. Heinz_, Jul 30 2019