OFFSET
1,1
COMMENTS
This can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":
1*3
4/(Pi-2) = 3 + --------------------
2*4
5 + ----------------
3*5
7 + ------------
4*6
9 + --------
11 + ... .
For a proof by humans see the arXiv:1907.00205 preprint linked below.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Gal Raayoni, George Pisha, Yahel Manor, Uri Mendlovic, Doron Haviv, Yaron Hadad, and Ido Kaminer, The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants, arXiv:1907.00205 [cs.LG], 2019-2020.
The Ramanujan Machine, Using algorithms to discover new mathematics.
EXAMPLE
3.50387678776821732240781940302290775850079601361148312728094190...
MAPLE
nn:= 126: # number of digits
b:= i-> `if`(i<2*nn, 2*i+1 +i*(i+2)/b(i+1), 1):
evalf(b(1), nn);
MATHEMATICA
RealDigits[4/(Pi-2), 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Jul 11 2019
STATUS
approved