login
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

%I #17 Apr 18 2021 13:57:09

%S 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,

%T 52,60,60,64,65,72,72,77,78,86,88,91,92,100,100

%N 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

%C 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?

%C 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).

%H PuzzleUp, <a href="/A165885/a165885.png">2009 No 10, Coins</a>

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

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

%K nonn,more

%O 0,4

%A _David Bevan_, Sep 29 2009