A368476 Decimal expansion of 109/65, being the highest possible win/loss points ratio in a completed 3-set tennis match, with 10-point final tie-break, which the player loses.

1, 6, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7

Offset

1,2

Comments

Tie-break games are played to 7 points in all sets except the last of the match, which is a 10-point tie-break.

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 8-10 in the two tie-break games.

Player A wins 109 points and player B wins 65 points, but player A loses the match.

This ratio is a little lower than when the final tie-break is played to 7 points (see A368009).

Links

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

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

Formula

Equals (6*4 + (6*4 + 6*2 + 5) + (6*4 + 6*2 + 8))/((6*4 + 7) + (6*4 + 10)).

Example

1.6769230... (periodic part 769230).

Mathematica

First[RealDigits[109/65, 10, 100]] (* or *)
PadRight[{1, 6}, 100, {3, 0, 7, 6, 9, 2}] (* Paolo Xausa, Jan 30 2024 *)

Crossrefs

Cf. A368008, A368009, A368146.

Apart from leading digits the same as A021017.

Sequence in context: A336002 A223172 A340153 * A115096 A132957 A339135

Adjacent sequences: A368473 A368474 A368475 * A368477 A368478 A368479

Keyword

nonn,cons,easy

Author

Marco Ripà, Dec 26 2023

Status

approved