This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309091 #54 Jun 29 2023 09:03:00 %S A309091 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 A309091 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 A309091 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 A309091 Decimal expansion of 4/(Pi-2). %C A309091 This can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine": %C A309091 1*3 %C A309091 4/(Pi-2) = 3 + -------------------- %C A309091 2*4 %C A309091 5 + ---------------- %C A309091 3*5 %C A309091 7 + ------------ %C A309091 4*6 %C A309091 9 + -------- %C A309091 11 + ... . %C A309091 For a proof by humans see the arXiv:1907.00205 preprint linked below. %H A309091 Alois P. Heinz, <a href="/A309091/b309091.txt">Table of n, a(n) for n = 1..10000</a> %H A309091 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 A309091 The Ramanujan Machine, <a href="http://www.ramanujanmachine.com/">Using algorithms to discover new mathematics</a>. %H A309091 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>. %e A309091 3.50387678776821732240781940302290775850079601361148312728094190... %p A309091 nn:= 126: # number of digits %p A309091 b:= i-> `if`(i<2*nn, 2*i+1 +i*(i+2)/b(i+1), 1): %p A309091 evalf(b(1), nn); %t A309091 RealDigits[4/(Pi-2), 10, 120][[1]] (* _Amiram Eldar_, Jun 29 2023 *) %Y A309091 Cf. A000796, A005563, A144396, A309419, A309420. %K A309091 nonn,cons %O A309091 1,1 %A A309091 _Alois P. Heinz_, Jul 11 2019