OFFSET
1,1
COMMENTS
For every n a cardinality of S has to be found such that the number of all possible nonempty proper subsets of S is greater than the number of all possible sums of the elements of those subsets. When it becomes so, the pigeonhole principle guarantees there are two disjoint subsets of S with the same sum of elements.
REFERENCES
a(2) is mentioned in Miklós Bóna, A Walk Through Combinatorics, Second ed., World Scientific Publishing, 2006, p. 28., s.e. 25.
MATHEMATICA
f[1]=5;
f[n_]:=f[n]=Module[{startingCardinality=f[n-1]+1},
While[
(2^startingCardinality)-2<= Sum[(10^n)-i, {i, 1, startingCardinality-1}]-10^(n-1)+1,
startingCardinality++
];
startingCardinality
];
f/@Range[70]
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Ivan N. Ianakiev, Aug 01 2016
STATUS
approved