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Search: id:A165885
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| A165885 |
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Minimum sum of a set of positive integers such that every positive integer <= n is the sum of 1 or 2 elements of the set |
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+0
2
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| 0, 1, 1, 3, 3, 6, 6, 8, 8, 12, 12, 15, 15, 19, 20, 24, 24, 30, 30, 34, 35, 41, 42, 47, 47, 52, 52, 60, 60, 64, 65, 72, 72, 77, 78, 86, 88, 91, 92, 100, 100
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If it is possible to make every value from 1 to n using at most 2 of the coins used in a country, what is the minimum possible value of the sum of the coins in this country?
By considering sets {1, 2, ..., r, 2r, 3r, ..., (s-1)r}, it is conjectured that the asymptotic behaviour is a(n) ~ 3/4 * 2^(1/3) * n^(4/3).
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LINKS
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PuzzleUp, Coins
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EXAMPLE
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a(8) = 8: {1,3,4}
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MATHEMATICA
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a[n_] := Min[Total /@ Select[Subsets[Range[n], Floor[(n + 1)/2]], Complement[Range[n], Total /@ Join[Subsets[ #, {1, 2}], Transpose[{#, #}]]] == {} &]]
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CROSSREFS
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Sequence in context: A127739 A070318 A023842 this_sequence A061795 A110261 A049318
Adjacent sequences: A165882 A165883 A165884 this_sequence A165886 A165887 A165888
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KEYWORD
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nonn
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AUTHOR
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David Bevan (dbevan(AT)emtex.com), Sep 29 2009
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