The Hailstone sequence of numbers can be generated from a starting positive integer,   n   by:

   If   n   is     1     then the sequence ends.
   If   n   is   even then the next   n   of the sequence    = n/2 
   If   n   is   odd   then the next   n   of the sequence    = (3 * n) + 1 


The (unproven) Collatz conjecture is that the hailstone sequence for any starting number always terminates.



This sequence was named by Lothar Collatz in 1937   (or possibly in 1939),   and is also known as (the):

   hailstone sequence,   hailstone numbers
   3x + 2 mapping,   3n + 1 problem
   Collatz sequence
   Hasse's algorithm
   Kakutani's problem
   Syracuse algorithm,   Syracuse problem
   Thwaites conjecture 
   Ulam's problem


The hailstone sequence is also known as   hailstone numbers   (because the values are usually subject to multiple descents and ascents like hailstones in a cloud).



Task

 Create a routine to generate the hailstone sequence for a number.
 Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1
 Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.
   (But don't show the actual sequence!)


See also

   xkcd (humourous).
   The Notorious Collatz conjecture Terence Tao, UCLA (Presentation, pdf).
   The Simplest Math Problem No One Can Solve Veritasium (video, sponsored).


 
'function arguments: "num" is the number to sequence and "return" is the value to return - "s" for the sequence or 
'"e" for the number elements.
Function hailstone_sequence(num,return)
    n = num
	sequence = num
	elements = 1
	Do Until n = 1
		If n Mod 2 = 0 Then
			n = n / 2
		Else
			n = (3 * n) + 1
		End If
		sequence = sequence & " " & n
		elements = elements + 1	
	Loop
	Select Case return
		Case "s"
			hailstone_sequence = sequence
		Case "e"
			hailstone_sequence = elements
	End Select
End Function
 
'test driving.
'show sequence for 27
WScript.StdOut.WriteLine "Sequence for 27: " & hailstone_sequence(27,"s")
WScript.StdOut.WriteLine "Number of Elements: " & hailstone_sequence(27,"e")
WScript.StdOut.WriteBlankLines(1)
'show the number less than 100k with the longest sequence
count = 1
n_elements = 0
n_longest = ""
Do While count < 100000
	current_n_elements = hailstone_sequence(count,"e")
	If current_n_elements > n_elements Then
		n_elements = current_n_elements
		n_longest = "Number: " & count & " Length: " & n_elements
	End If
	count = count + 1
Loop
WScript.StdOut.WriteLine "Number less than 100k with the longest sequence: "
WScript.StdOut.WriteLine n_longest
 