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

Offset: 1

Author

Alois P. Heinz, Jul 30 2019

Keywords

• nonn
• cons

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 - ... .

Examples

			2.80745499308537947657159669392697176828889127774792...
		

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

Crossrefs

Cf. A000796, A309091, A309419.

Programs

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 *)