We have a list of prices and need to find both the number of clusters (or intervals) and the mean price of each cluster (or interval). The only constraint is that we want cluster means to be at least X distance from each another.
K-means doesn't seem to work because it requires specifying the number of clusters as input.
The reason for finding these is that prices become a "significant" cluster with more data points serve as support and resistance levels for trading. Currently this process is done by simple human observation of clusters of prices on a chart. But the purpose here is to quantify this in an algorithm to make it more objective and measurable.