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A165885 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 2
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; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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 behavior is a(n) ~ 3/4 * 2^(1/3) * n^(4/3).

LINKS

Table of n, a(n) for n=0..40.

PuzzleUp, 2009 No 10, Coins

EXAMPLE

a(8) = 8: {1,3,4}

MATHEMATICA

a[n_] := Min[Total /@ Select[Subsets[Range[n], Floor[(n + 1)/2]], Complement[Range[n], Total /@ Join[Subsets[ #, {1, 2}], Transpose[{#, #}]]] == {} &]]

CROSSREFS

Sequence in context: A219381 A219852 A023842 * A227128 A061795 A110261

Adjacent sequences:  A165882 A165883 A165884 * A165886 A165887 A165888

KEYWORD

nonn,more

AUTHOR

David Bevan, Sep 29 2009

STATUS

approved

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Last modified October 28 16:41 EDT 2021. Contains 348329 sequences. (Running on oeis4.)