fixed_explain.coffee

# set l to Math.log because you use it twice
l = Math.log
# create a recursive function, r, to iterate on a chain until it reaches a fixed point
# n is the input for the current iteration
r = (n)->
	###
		This next line is a mouthful. "l(n)/l 2" computes the log base 2 of n. This is the index of the highest set bit in n
		The reduce function is basically a sum across the bits of the number.
		It adds 3 to the sum if the bit is set ("one".length) and 4 if the bit is not set ("zero".length)
		So, in a nutshell, z is set to the number of letters in the binary phrase for the number n
	###
	z = [0..l(n)/l 2].reduce((a,b)->`1<<b&n?3+a:4+a`),0)
	# if a fixed point has been reached, return it. else, call this function on z
	`z==n?n:r(z)`
# create hash
c = {}
# for 1 to 1 million...
[1..1000000].map (n)->
	# use the r function to find the fixed point.
	# initialize the c hash value for that key to zero
	c[r n]?=0
	# increment value
	c[r n]++
# output hash
c