A309420 - OEIS

A309420

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

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, 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, 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

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OFFSET

1,1

COMMENTS

Conjecturally, this can be computed using a recursion formula discovered by an algorithm called "The Ramanujan Machine":

1*1

4/(3*Pi-8) = 3 - --------------------

2*3

6 - ----------------

3*5

9 - ------------

4*7

12 - --------

15 - ... .

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, 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

Index entries for transcendental numbers

EXAMPLE

2.80745499308537947657159669392697176828889127774792...

MAPLE

nn:= 126: # number of digits

# b:= i-> `if`(i<4*nn, 3*i -i*(2*i-1)/b(i+1), 1):

# evalf(b(1), nn);

evalf(4/(3*Pi-8), nn);

MATHEMATICA

RealDigits[4/(3 Pi-8), 10, 120][[1]] (* Harvey P. Dale, May 09 2021 *)

CROSSREFS