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%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
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