Coffeescript - Improve algorithm for increasing grouping - coffeescript

Question

The code below works but I am wondering if there is a better way that maybe uses some of the features of coffeescript that I am unfamiliar with.
The problem is this, I need to page items but the paging increases each time.
If I take the number 20 for example, it would create the following pages:
1 - 3
4 - 7
8 - 15
16 - 20
I have the following test and code which does pass:
module 'Remainder',
setup: ->
#remainder = 20
test 'splits remainder incrementally', ->
parts = #remainder.increasingSplit()
equal parts[0], '1 - 3', ''
equal parts[1], '4 - 7', ''
equal parts[2], '8 - 15', ''
equal parts[3], '16 - 20', ''
Number.prototype.increasingSplit = ->
start = 1
nextSplit = 3
parts = []
finished = false
while !finished
if nextSplit > #
parts.push "#{start} - #{#}"
break
parts.push "#{start} - #{nextSplit}"
start = nextSplit + 1
nextSplit = nextSplit * 2 + 1
parts

Answer 1

Without changing the algorithm too much, you can try this:
Number::increasingSplit = ->
start = 1
nextSplit = 3
parts = []
while start <= #
parts.push "#{start} - #{Math.min nextSplit, #}"
start = nextSplit + 1
nextSplit = nextSplit * 2 + 1
parts
The changes were:
replacing .prototype with ::,
removing of the finished variable (which was not being used effectively because the break anyway) and the break altogether and changing the condition to start <= #,
using only one parts.push <part>, with the minimum between nextSplit and # as the top.
Also, i'd advice against extending the Number prototype in this case. Extending the prototype of primitive types can sometimes cause weird problems, like:
Number::isFour = -> # is 4
console.log 4.isFour() # -> false
That happens because inside that function # will be a Number object instead of a primitive number, thus making the === 4 comparison always fail. That would not happen if you define isFour as a standalone function:
isFour = (n) -> n is 4
console.log isFour 4 # -> true
So, i'd prefer this version of incrasingSplit:
increasingSplit = (n) ->
start = 1
nextSplit = 3
parts = []
while start <= n
parts.push "#{start} - #{Math.min nextSplit, n}"
start = nextSplit + 1
nextSplit = nextSplit * 2 + 1
parts
Finally, if you don't mind recursion, you can go with a more FP-style algorithm :)
increasingSplit = (n, start = 1, nextSplit = 3) ->
if start > n
[]
else
part = "#{start} - #{Math.min nextSplit, n}"
rest = increasingSplit n, nextSplit + 1, nextSplit * 2 + 1
[part, rest...]