Different upper and lower bound - Revision history

Tomtom2357 at 06:48, 1 May 2015

2015-05-01T06:48:15Z

← Older revision		Revision as of 23:48, 30 April 2015
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	Question: is <math>N(1,b)</math> always prime?		Question: is <math>N(1,b)</math> always prime?

	<math>N(2, 2) ~~\geq 1124~~</math> (e.g [[the first 1124-sequence]])		<math>N(2, 2) = 1160</math> (e.g [[the first 1124-sequence]])

	For the zero-based problem, see [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4822 this comment]		For the zero-based problem, see [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4822 this comment]

2015-03-15T01:41:50Z

Updated page for maximum discrepancy 2 sequence

2010-01-12T13:08:11Z

added Jason's derivation of N(1,1)

← Older revision		Revision as of 06:08, 12 January 2010
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	<math>N(0, b) = b</math> (everything must be <math>+1</math>)		<math>N(0, b) = b</math> (everything must be <math>+1</math>)

	<math>N(1, 1) = 11</math> (there are <math>4</math> such sequences: choose <math>x_1</math>, and use the constraints <math>x_n +x_{2n} = 0</math> and <math>x_1 + \ldots + x_{2n} = 0</math> to determine the entries up to <math>10</math>; then choose <math>x_{11}</math>)		<math>N(1, 1) = 11</math> (there are <math>4</math> such sequences: choose <math>x_1</math>, and use the constraints <math>x_n +x_{2n} = 0</math> and <math>x_1 + \ldots + x_{2n} = 0</math> to determine the entries up to <math>10</math>; then choose <math>x_{11}</math>) (alternatively: Our first placement can be arbitrary, so suppose 6 is +. This forces 12-, which forces 3- and 9+, which forces 2- and 4+, which forces 1+ and 8-, which forces 5- and 10+, which forces 7+, and a contradiction when d = 1 and k = 10. The sequence is thus: + – - + – + + – + + . -)

	<math>N(1, 2) = 41</math> (there are <math>4</math> such sequences -- example below)		<math>N(1, 2) = 41</math> (there are <math>4</math> such sequences -- example below)

2010-01-10T09:02:20Z

Added question on primality of N(1,b)

← Older revision		Revision as of 02:02, 10 January 2010
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	<math>N(1,b)<\infty</math> ([http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov])		<math>N(1,b)<\infty</math> ([http://www.dpmms.cam.ac.uk/~ardm/erdoschu.pdf On a conjecture of Erdős and Čudakov])

			Question: is <math>N(1,b)</math> always prime?

	<math>N(2, 2) \geq 1124</math> (e.g [[the first 1124-sequence]])		<math>N(2, 2) \geq 1124</math> (e.g [[the first 1124-sequence]])

	For the zero-based problem, see [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4822 this ~~commend~~]		For the zero-based problem, see [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4822 this comment]

	==Method==		==Method==
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	--[[User:Alec\|Alec]] 13:46, 9 January 2010 (UTC)		--[[User:Alec\|Alec]] 13:46, 9 January 2010 (UTC)


	==Relevant code==		==Relevant code==

	The code(s) (or a link to the code(s)) used to find this sequence should be posted here.		The code(s) (or a link to the code(s)) used to find this sequence should be posted here.

2010-01-09T19:00:37Z

Status

← Older revision		Revision as of 12:00, 9 January 2010
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	== Status ==		== Status ==

	Is the data still relevant (e.g. longest know)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere?		Is the data still relevant (e.g. longest know)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere?

	~~The sequence is the longest know sequence with discrepancy 2.~~

	== The data==		== The data==

2010-01-09T18:46:59Z

← Older revision		Revision as of 11:46, 9 January 2010
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	<math>N(2, 2) \geq 1124</math> (e.g [[the first 1124-sequence]])		<math>N(2, 2) \geq 1124</math> (e.g [[the first 1124-sequence]])

			For the zero-based problem, see [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4822 this commend]

	==Method==		==Method==