In one dimensional data, don't use cluster analysis.
Cluster analysis is usually a multivariate technique. Or let me better put it the other way around: for one-dimensional data -- which is completely ordered -- there are much better techniques. Using k-means and similar techniques here is a total waste, unless you put in enough effort to actually optimize them for the 1-d case.
Just to give you an example: for k-means it is common to use k random objects as initial seeds. For one dimensional data, it's fairly easy to do better by just using the appropriate quantiles (1/2k, 3/2k, 5/2k etc.), after sorting the data once, and then optimize from this starting point. However, 2D data cannot be sorted completely. And in a grid, there likely will be empty cells.
I also wouldn't call it cluster. I would call it interval. What you really want to do is to optimize the interval borders. If you do k-means, it will test for each object if it should be moved to another cluster. That does not make sense in 1D: only the objects at the interval borders need to be checked. That obviously is much faster, as there are only ~2k objects there. If they do not already prefer other intervals, more central objects will not either.
You may want to look into techniques such as Jenks Natural Breaks optimization, for example.
Or you can do a kernel density estimation and look for local minima of the density to split there. The nice thing is that you do not need to specify k for this!
See this answer for an example how to do this in Python (green markers are the cluster modes; red markers a points where the data is cut; the y axis is a log-likelihood of the density):
P.S. please use the search function. Here are some questions on 1-d data clustering that you missed: