Strange - using your randomEntry function, the first odd numbers don't start showing up until 53668, and then it's odd numbers for a while. An example from the REPL:
> List.range 0 100000 |> List.map randomEntry |> List.filter (\(a,b) -> b % 2 /= 0) |> List.take 10
[(53668,35),(53669,87),(53670,1),(53671,15),(53672,29),(53673,43),(53674,57),(53675,71),(53676,85),(53677,99)]
: List ( Int, Int )
Now I can't tell you why there is such stickiness in this range (here's the source for the int generator if you're curious), but hopefully I can shed some light on randomness in Elm.
There is really no way to create a truly random number generator using standard computing technology (quantum computers aside), so the typical way of creating randomness is to provide a function that takes a seed value, returns a pseudo-random number and the next seed value to use.
This makes random number generation predictable, since you will always get the same "random" number for the same seed.
This is why you always get identical results for the input you've given: You are using the same seed values of 0 through 1000. In addition, you are ignoring the "next seed" value passed back from the step function, which is returned as the second value of the tuple.
Now, when dealing with random number generators, it is a good rule of thumb to avoid dealing with the seed as much as possible. You can write generators without referring to seeds by building on smaller generators like int, list, and so on.
The way you execute a generator is either by returning a Cmd generated from Random.generate from your update function, which leaves the responsibility of deciding which seed to use to the Elm Architecture (which probably uses some time-based seed), or you can pass in the seed using Random.step, which you've done above.
So, going back to your original example, if you were to write a generator for returning a list of random numbers of a certain size, where each number is within a certain range, it could look something like this:
randomListGenerator : Int -> (Int, Int) -> Random.Generator (List Int)
randomListGenerator size (low, high) =
Random.list size (Random.int low high)
Executing this using step in the REPL shows how it can be used:
> initialSeed 0 |> step (randomListGenerator 20 (1, 10)) |> Tuple.first
[6,6,6,1,3,10,4,4,4,9,6,3,5,3,7,8,3,4,8,5] : List Int
You'll see that this includes some odd numbers, unlike your initial example. The fact that it is different than your example is because the generator returns the next seed to use each consecutive step, whereas your example used the integers 0 through 1000 in order. I still have no explanation to your original question of why there is such a big block of evens using your original input, other than to say it is very odd.