Sum-free sequence

Sum-free sequence

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

:{n_k}_{kinmathbb N}

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

This definition is due to Paul Erdős, 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.


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