9,7,4,2: The random seed correlation

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Summary:

Discovering seed values for special random numbers.

9,7,4,2: The random seed correlation

CloudVariable 02 Nov 2018 03:10

I have spent the past few days sorting through random number and seed patterns, and I have discovered some really neat properties to relate them. This entire series of research is regarding the little collab between Deoxal and I regarding the correlation between the random numbers and their seeds. Anybody who wants to help can help by attempting to prove these wrong, or at least giving more insight on the particular conjecture. I intend to add more posts to this thread with more conjectures.

N represents the first random number generated by an nonnegative integer seed S
The random seed function inputs a seed, and outputs the first random number that the generator returns with that given seed value.

Conjecture #1- the 9,7,4,2 pattern

For every value of S less than 13, round(10N,1) will always be approximately equal to either 9,7,4,2. The pattern oscillates until S=13, but the relationship remains reasonably approximate for much longer, slowly growing more inaccurate until it is almost completely flawed.

The following conjecture has been rewritten to better explain the point after a helpful comment by Deoxal
Conjecture #2- the largest gaps between the random seeds occur between numbers divisible by 58 and 59. For small seed values the 59 divisible seeds are (usually) the biggest, but since this pattern seems to shift downward over time, it probably isn’t an important way to find 1 valued random seed functions.

Last edited on 02 Nov 2018 14:30 by CloudVariable Show more

Re: 9,7,4,2: The random seed correlation

kg583 02 Nov 2018 04:13

Assuming I've read your descriptions right, the following code should be able to find a counterexample to your conjecture if it exists:

:S→rand
:While 1
:10round(rand,1
:Ans→rand
:Pause Ans
:End

for some starting integer S. It isn't too hard to prove that every integer S eventually leads to the loop (2,5,7), though the intermediate steps are a bit harder to track. I think the CE has a slightly varied PRNG, because I've seen 5's but no 4's and 10's but no 9's (i.e. just one off from your conjecture).

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The solution to a complex problem is often a simple answer.

Re: 9,7,4,2: The random seed correlation

Deoxal 02 Nov 2018 06:30

With regards to your first conjecture, you may be overplaying that pattern's significance, apparently prime numbers have this pattern where primes ending in a given digit are less likely to be neighbors with primes that end with that same digit, and it too peters off the higher you go.

As for your second conjecture, you definitely need to formalize and revise it because 196164532 kind of outputs 1 one from rand and it is not divisible by 59. That was a value I was initially looking for with my code, because I didn't read the page close enough I wrote the code before finding it there, but there could be more than one so it's still useful. I say kind of because randBin( and randNorm( would have some sort of problem if the output was actually 1, according to the rand page anyway. This is the part that actually confused me when I posted this since rand doesn't use its own output as the next argument to itself(at least not by itself). I linked to this before but I think it's worth posting here again. I can't understand the C++ or Python very well since I haven't coded in them before but I probably wouldn't understand it if it was in Java either. A free PDF is also linked to on the page about rand. Reading it would really help in understanding how to make good conjectures and then how to prove them(again a bit hard to understand but not impossible).

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4920616D204261746D616E

Re: 9,7,4,2: The random seed correlation

CloudVariable 02 Nov 2018 14:24

Thanks for the link. I realized after I had written this that the conjectures are only approximate, and they appear to break down as the seed values increase. Although the patterns change, I meant to stress the importance of the oscillation patterns (the differences between them) rather than their standalone values. I did find something particularly interesting, however, in the upper limit of the seed. Seeds above 1e10 appear to produce the same random seed function. Additionally, look at the pattern in the random seed functions of the powers of ten until that point. They appear to be some sort of a shifted sequence, but only for a few digits. I won’t list the values here, but the familiar part of the sequence ends in 24. And finally, I found you a near zero value. It doesn’t round to zero, but it nearly does. The seed value is 98082266, which happens to be 196164532 divided by 2. It is approximately 3.8e-8.

Last edited on 02 Nov 2018 14:51 by CloudVariable Show more

Re: 9,7,4,2: The random seed correlation

Deoxal 02 Nov 2018 15:29

Seeds above 1e10 appear to produce the same random seed function.

This is because the calculator exclusively uses floating point numbers in all of its calculations despite the fact that the z80 instruction set does not natively support floating point calculations. Floating point numbers represent smaller numbers more precisely than large numbers. The following will produce different outputs.

3e10→rand
rand
5e10→rand
rand

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4920616D204261746D616E

Last edited on 02 Nov 2018 15:49 by Deoxal Show more

Re: 9,7,4,2: The random seed correlation

CloudVariable 02 Nov 2018 04:46

Sorry, I wasn’t very careful in defining it. The relationship is definite until S=13, but remains approximate for much longer. I made sure to edit the post. I went through the same code as well. I doubt that the PRNG is different on the CE because I have tested it with other calculators, but I would really appreciate it if you had any specific examples to share so I can see if they are the same on mine.