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A309091 Decimal expansion of 4/(Pi-2). 3
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
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, Ido Kaminer, The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants, arXiv:1907.00205 [cs.LG], 2019.

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);

CROSSREFS

Cf. A000796, A005563, A144396, A309419, A309420.

Sequence in context: A010614 A153099 A102575 * A200520 A224933 A307209

Adjacent sequences:  A309088 A309089 A309090 * A309092 A309093 A309094

KEYWORD

nonn,cons

AUTHOR

Alois P. Heinz, Jul 11 2019

STATUS

approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)