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%I #54 Jun 29 2023 09:03:00
%S 3,5,0,3,8,7,6,7,8,7,7,6,8,2,1,7,3,2,2,4,0,7,8,1,9,4,0,3,0,2,2,9,0,7,
%T 7,5,8,5,0,0,7,9,6,0,1,3,6,1,1,4,8,3,1,2,7,2,8,0,9,4,1,9,0,0,2,7,9,9,
%U 6,5,7,7,4,0,8,7,4,2,1,9,9,0,2,6,9,0,3,3,5,0,3,7,6,7,0,8,9,1,4,3,9,8,2,9,1
%N Decimal expansion of 4/(Pi-2).
%C This can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":
%C 1*3
%C 4/(Pi-2) = 3 + --------------------
%C 2*4
%C 5 + ----------------
%C 3*5
%C 7 + ------------
%C 4*6
%C 9 + --------
%C 11 + ... .
%C For a proof by humans see the arXiv:1907.00205 preprint linked below.
%H Alois P. Heinz, <a href="/A309091/b309091.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>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e 3.50387678776821732240781940302290775850079601361148312728094190...
%p nn:= 126: # number of digits
%p b:= i-> `if`(i<2*nn, 2*i+1 +i*(i+2)/b(i+1), 1):
%p evalf(b(1), nn);
%t RealDigits[4/(Pi-2), 10, 120][[1]] (* _Amiram Eldar_, Jun 29 2023 *)
%Y Cf. A000796, A005563, A144396, A309419, A309420.
%K nonn,cons
%O 1,1
%A _Alois P. Heinz_, Jul 11 2019
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