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A309420 Decimal expansion of 4/(3*Pi-8).

%I A309420 #20 Oct 01 2022 00:18:52
%S A309420 2,8,0,7,4,5,4,9,9,3,0,8,5,3,7,9,4,7,6,5,7,1,5,9,6,6,9,3,9,2,6,9,7,1,
%T A309420 7,6,8,2,8,8,8,9,1,2,7,7,7,4,7,9,2,0,5,9,6,1,4,3,0,5,7,5,2,5,3,2,0,7,
%U A309420 9,4,1,4,2,1,7,9,9,9,0,5,7,0,8,8,2,9,5,2,4,4,1,3,9,3,8,1,0,6,0,1,7,1,5,1
%N A309420 Decimal expansion of 4/(3*Pi-8).
%C A309420 Conjecturally, this can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":
%C A309420                                 1*1
%C A309420     4/(3*Pi-8)  =  3 - --------------------
%C A309420                                   2*3
%C A309420                        6 - ----------------
%C A309420                                     3*5
%C A309420                            9 - ------------
%C A309420                                       4*7
%C A309420                                12 - --------
%C A309420                                     15 - ...  .
%H A309420 Alois P. Heinz, <a href="/A309420/b309420.txt">Table of n, a(n) for n = 1..10000</a>
%H A309420 Gal Raayoni, George Pisha, Yahel Manor, Uri Mendlovic, Doron Haviv, Yaron Hadad, 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 A309420 The Ramanujan Machine, <a href="http://www.ramanujanmachine.com/">Using algorithms to discover new mathematics</a>
%H A309420 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A309420 2.80745499308537947657159669392697176828889127774792...
%p A309420 nn:= 126: # number of digits
%p A309420 # b:= i-> `if`(i<4*nn, 3*i -i*(2*i-1)/b(i+1), 1):
%p A309420 # evalf(b(1), nn);
%p A309420 evalf(4/(3*Pi-8), nn);
%t A309420 RealDigits[4/(3 Pi-8),10,120][[1]] (* _Harvey P. Dale_, May 09 2021 *)
%Y A309420 Cf. A000796, A309091, A309419.
%K A309420 nonn,cons
%O A309420 1,1
%A A309420 _Alois P. Heinz_, Jul 30 2019