Type-Level FizzBuzz in Typescript

FizzBuzzIterator.d.ts

// Iterator approach, seems to be good up until ~850
type Result = Take<100, FizzBuzzIterator[1]>
// ["1", "2", "Fizz", "4", "Buzz", "Fizz", "7",  "8", "Fizz", "Buzz", "11", "Fizz", "13", "14", "FizzBuzz", ...]

export type FizzBuzzIterator<
  S extends Record<any, any> = { 3: []; 5: []; i: [] },
  R extends string = `${S[3]["length"] extends 3 ? "Fizz" : ""}${S[5]["length"] extends 5 ? "Buzz" : ""}`
> = [
  R extends "" ? `${S["i"]["length"]}` : R,
  FizzBuzzIterator<{
    3: S[3]["length"] extends 3 ? [1] : [...S[3], 1]
    5: S[5]["length"] extends 5 ? [1] : [...S[5], 1]
    i: [...S["i"], 1]
  }>
]

type Take<N extends number, Cons extends [any, any], Acc extends any[] = []>
  = Acc["length"] extends N ? Acc : Take<N, Cons[1], [...Acc, Cons[0]]>

FizzBuzzRange.d.ts

// Normal recursive approach, seems to be good up until ~850
type Result = FizzBuzzRange<1, 101>
// ["1", "2", "Fizz", "4", "Buzz", "Fizz", "7",  "8", "Fizz", "Buzz", "11", "Fizz", "13", "14", "FizzBuzz", ...]

export type FizzBuzzRange<A extends number, B extends number, Acc extends any[] = []>
  = A extends B ? Acc : FizzBuzzRange<Add<A, 1>, B, [...Acc, FizzBuzz<A>]>

export type FizzBuzz<
  X extends number,
  S extends string = `${Div<X, 3> extends true ? "Fizz" : ""}${Div<X, 5> extends true ? "Buzz" : ""}`
> = S extends "" ? `${X}` : S

type Div<A extends number, B extends number, Acc extends number = B>
  = A extends Acc ? true : Lt<A, Acc> extends true ? false : Div<A, B, Add<Acc, B>>

type Add<A extends number, B extends number> = Extract<[...Range<A>, ...Range<B>]["length"], number>

type Range<N extends number, Acc extends number[] = []>
  = Acc["length"] extends N ? Acc : Range<N, [...Acc, Acc["length"]]>

type Lt<A extends number, B extends number, R extends number[] = Range<B>> = A extends R[number] ? true : false