Creating simple experiment from function without "data" argument

I am struggling to design an experiment using my own function, which I will try to illustrate here using a function piApprox() from Example 1 from "Get Started":

piApprox = function(n) {
  nums = matrix(runif(2 * n), ncol = 2)
  d = sqrt(nums[, 1]^2 + nums[, 2]^2)
  4 * mean(d <= 1)
}

I now want to create and run 50 jobs using piApprox() in a way they will satisfy 3 conditions:

1. I want to run piApprox() with 5 different values of parameter n: n1=1000, n2=2000, n3=3000, n4=4000, n5=5000, with 10 jobs created for each value of n

2. Each of these 5 parametrizations to start from seed=1 so these 5 sets of results stay stochastically comparable

3. For convenience, I want to keep all the code for definition/configuration of this example as single R script, ideally creating only a single registry

My first solution is to run all 5*10 jobs together like this:

reg = makeRegistry(file.dir = NA, seed = 1)
batchMap(fun = piApprox, n = rep(1:5, each=10)*1000)

Upper solution would satisfy conditions 1 and 3, but not the important condition 2 about seeding

My second solution I can think of is to create five separate scripts/registers each with separate value of parameter n, satisfying conditions 1 and 2, but tedious to set up and collect results

Now I believe this is possible to define this assignment using addProblem(), addAlgorithm(), addExperiment() functions in a way the solution would satisfy my 3 aforementioned conditions. But as a beginner, I am struggling to come up with such solution (e.g. what can I pass as the data parameter to addProblem(), when piApprox() is generating its own data?).

I think that an exercise similar to what I am describing could serve as helpful bridging example between simplest Example1 and more advanced Example2.

Start by comparing the batchtools “Get Started” Example 1 and Example 2, then read the roles of addProblem(), addAlgorithm(), and addExperiment(). The example is done when one R script and registry demonstrate five n values, ten jobs per value, comparable seeds, and collected results without requiring a data argument.