What kind of PRNG would match such scatter plots?

I've been given the challenge to find the seed from a series of pseudo-randomly generated alphanumerical IDs and after some analysis, I'm stuck in a dead end that I hope you'll be able to get me out of.

Each ID is obtained by passing the previous one through the encryption algorithm, that I'm supposed to reverse engineer in order to find the seed. The list given to me is composed of the 2070 first IDs (without the seed obviously). The IDs start as 4 alphanumerical characters, and switch to 5 after some time (e.g. "2xm1", "34nj", "avdfe", "2lgq9")

My first reflex was to try to convert those IDs from base36 to some other base, notably decimal. I used the results to scatter plot a chart of the IDs' decimal values in terms of their rank in the list, when I noticed a pattern that I couldn't understand the origin of.

After isolating the two parts of the list in terms of ID length, I scatter plotted the same graph for the 4-characters IDs sub-list and 5-characters IDs sub-list, allowing me to notice the strange density patterns.

After some analysis, I've observed 2 things :

• For each sub-list, the delimitation between the 2 densities is 6x32^(n-1), n being the number of characters in the ID. In other terms, it is 1/6th of the entire range of values for a given ID length.
• The repartition of those IDs in relation to this limit tends towards 50/50, half of them being above the 1/6th limit, half of them being under it.

I've tried to correlate such a behavior with other known PRNG scatter-plots, but none of them matched what I get on my graphs.

I'm hoping some of you might know about an encryption method, formula, or function matching such a specific scatter plot, or have any idea about what could be going on behind the scenes.

Thanks in advance for your answers.