A181534 Minimum number of rounds to be played to decide a two-player game of up to n rounds in which the winner of round j receives j points.

1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 48

Offset

1,2

Comments

The game described above is played in the German TV Show 'Schlag den Raab'.

a(n) is the least k such that 2*A000217(k) > A000217(n). - Peter Kagey, Nov 07 2016

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Example

For n = 15, the maximum number of rounds per game in the show, a(n) = 11. So there are at least eleven rounds to be played in each game.

Mathematica

Table[ Ceiling[ -1/2 + Sqrt[1/4 + 2 Ceiling[(n^2 + n + 2)/4]]], {n, 1, 50} ]

Prog

(PARI) a(n)=ceil(sqrt((n^2 + n + 5)\4*2+1/4)-1/2) \\ Charles R Greathouse IV, Jun 19 2013

Crossrefs

Sequence in context: A121928 A175406 A210435 * A258703 A067022 A113818

Adjacent sequences: A181531 A181532 A181533 * A181535 A181536 A181537

Keyword

nice,nonn,easy

Author

Oliver Gronau (ogronau(AT)web.de), Oct 29 2010

Extensions

More terms from Colin Barker, May 29 2013

Status

approved