Problem 42355. Minimum Set (A+A)U(A*A) OEIS A263996

Created by Richard Zapor

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This Challenge is to find an integer vector A that creates the minimum set size for (A+A) U (A*A) for a given vector length,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://oeis.org/A263996\"><w:r><w:t>OEIS A263996</w:t></w:r></w:hyperlink><w:r><w:t>. The length, best value, Prime_max, and Value_max will be provided.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://oeis.org/A263996\"><w:r><w:t>OEIS A263996</w:t></w:r></w:hyperlink><w:r><w:t> gives the minimum set sizes thru length 50. Length 7 has best value 26 with Prime_max 5 and Value_max 8. A=[1 2 3 4 5 6 8] yields [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 24 25 30 32 36 40 48 64]. The</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://68.173.157.131/Contest/SumsAndProducts1/FinalReport\"><w:r><w:t>Al Zimmermann Sums Contest Final Report</w:t></w:r></w:hyperlink><w:r><w:t> extends A263996 for lengths 40:40:1000 with complete vector solutions. The contest winner, Rokicki, noted his method used P-smooth sets, hill climbing, and random swaps. The contest was a little tougher with only L given.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example Input/Output: L=9;Best=36;pmax=5;vmax=12; v = SP(L,Best,pmax,vmax); Yields v=[1 2 3 4 5 6 8 10 12]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Theory/Hints: The V superset is found using</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1298-p-smooth-numbers\"><w:r><w:t>psmooth(pmax,vmax)</w:t></w:r></w:hyperlink><w:r><w:t> . One observation is that for every v element the set v contains prod of all v element factor permutations. The time eater will be score evaluation. Residual evaluation suggested. A history screen, prior to score evaluation, of prior processed vectors is essential. A quick history pre-screen is vector sum. Replace testing of only values that are not factors of other numbers (eg 2,3 no replace) enables a reasonable time rolling score solution without random for the small test case values.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

This Challenge is to find an integer vector A that creates the minimum set size for (A+A) U (A*A) for a given vector length, <a href = "https://oeis.org/A263996">OEIS A263996</a>. The length, best value, Prime_max, and Value_max will be provided.The <a href = "https://oeis.org/A263996">OEIS A263996</a> gives the minimum set sizes thru length 50. Length 7 has best value 26 with Prime_max 5 and Value_max 8. A=[1 2 3 4 5 6 8] yields [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 24 25 30 32 36 40 48 64].
The <a href = "http://68.173.157.131/Contest/SumsAndProducts1/FinalReport">Al Zimmermann Sums Contest Final Report</a> extends A263996 for lengths 40:40:1000 with complete vector solutions. The contest winner, Rokicki, noted his method used P-smooth sets, hill climbing, and random swaps. The contest was a little tougher with only L given.Example Input/Output:
L=9;Best=36;pmax=5;vmax=12;
v = SP(L,Best,pmax,vmax); Yields v=[1 2 3 4 5 6 8 10 12]Theory/Hints: The V superset is found using <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1298-p-smooth-numbers">psmooth(pmax,vmax)</a> . One observation is that for every v element the set v contains prod of all v element factor permutations. The time eater will be score evaluation. Residual evaluation suggested. A history screen, prior to score evaluation, of prior processed vectors is essential. A quick history pre-screen is vector sum. Replace testing of only values that are not factors of other numbers (eg 2,3 no replace) enables a reasonable time rolling score solution without random for the small test case values.

Solve

Solution Stats

2 Solutions
2 Solvers

Last Solution submitted on Aug 30, 2017

Last 200 Solutions

Problem Recent Solvers2

Problem Tags

oeis psmooth zimmermann

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 42355. Minimum Set (A+A)U(A*A) OEIS A263996

Solution Stats

Last 200 Solutions

Problem Recent Solvers2

Suggested Problems

More from this Author241

Problem Tags

Community Treasure Hunt

Problem 42355. Minimum Set (A+A)U(A*A) OEIS A263996

Solution Stats

Last 200 Solutions

Problem Recent Solvers2

Suggested Problems

More from this Author241

Problem Tags

Community Treasure Hunt

Players