A368009 Decimal expansion of 53/31, being the highest possible points won/lost ratio in a completed 3-set tennis match which the player loses.

1, 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, 9, 3, 5

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 3 sets occurs with game scores 6-0 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 two tie-break games.

Player A wins 106 points and player B wins 62 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 (6*4 + 2*(6*4 + 6*2 + 5))/(2*(6*4 + 7)).

Example

1.709677419354838... (periodic part 709677419354838).

Mathematica

First[RealDigits[53/31, 10, 100]] (* Paolo Xausa, Jan 29 2024 *)

Crossrefs

Cf. A021428, A368008, A368146, A368476.

Sequence in context: A093444 A369522 A021858 * A368497 A348680 A014565

Adjacent sequences: A368006 A368007 A368008 * A368010 A368011 A368012

Keyword

nonn,cons,easy

Author

Marco Ripà, Dec 07 2023

Status

approved