In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a sum-free sequence is an increasing positive integer sequence

Sequence

In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...

such that for each , is never a sum of preceding elements of the same sequence.

This definition is due to Paul Erdős

Paul Erdos

Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...

, who was interested in finding sum-free sequences with a large sum of reciprocals.

An easy example of such a sequence

1, 2, 4, 8, 16, ...

The definition of sum-free sequence is different of that of sum-free set

Sum-free set

In additive combinatorics and number theory, a subset A of an abelian group G is said to be sum-free if the sumset A⊕A is disjoint from A...

.