A368008 Decimal expansion of 171/93, being the highest possible points won/lost ratio in a completed 5-set tennis match which the player loses.

1, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1, 9, 3, 5, 4, 8, 3, 8, 7, 0, 9, 6, 7, 7, 4, 1

Offset

1,2

Comments

Tie-break games are played to 7 points in all sets.

The structure of sets and games in tennis means a player can win more points but lose the match.

The highest win/loss ratio for 5 sets occurs with game scores 6-0 6-0 6-7 6-7 6-7 where player A wins games by points score 4-0, and loses by 2-4 in ordinary games and 5-7 in the three tie-break games.

Player A wins 171 points and player B wins 93 points, but player A loses the match.

Links

Table of n, a(n) for n=1..87.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Formula

Equals (2*6*4 + 3*(6*4 + 6*2 + 5))/(3*(6*4 + 7)).

Example

1.838709677419354... (periodic part 838709677419354).

Mathematica

First[RealDigits[171/93, 10, 100]] (* Paolo Xausa, Jan 30 2024 *)

Crossrefs

Cf. A021061, A368009, A368146, A368476.

Sequence in context: A085672 A019866 A006833 * A085011 A250129 A099724

Adjacent sequences: A368005 A368006 A368007 * A368009 A368010 A368011

Keyword

nonn,cons,easy

Author

Marco Ripà, Dec 07 2023

Status

approved