What is rufus numbers?

Rufus numbers are a sequence of natural numbers that are created by a simple rule. The first term in the sequence is 1, and every subsequent term is the smallest positive integer that cannot be expressed as the sum of a non-negative integer multiple of any of the previous terms. For example, the first few terms of the sequence are:

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, ...

The sequence is named after Karl Rufus, a German mathematician who described it in a paper published in 1918. Rufus numbers have been studied extensively in number theory and combinatorics, and have connections to various topics such as partitions of integers and modular arithmetic. Despite their seemingly random nature, the sequence has many interesting properties and open questions still remain about its behavior.