1 Come up with a clear and interesting conjecture concerning

1. Come up with a clear and interesting conjecture concerning primes or the \"Hailstone\" Sequence.

2. Write a program that will allow the user (you!) to gather data regarding the conjecture posed in (1) Using Visual Basics.

Solution

\' please run this program in version VB6 Standard
Dim flag As Boolean \' true to print values
Sub main()
    Dim longest As Long, n As Long
    Dim i As Long, value As Long

    Console.WriteLine(\"Enter some number :\")
    i = Console.ReadLine() \' provide value for sequence
    flag = True
  
        Console.WriteLine(\"Sequence length of \" + i + \" is \" +hailstonesSequence(i))
  
    flag = False
    longest = 0
    For i = 1 To 99999
        If longest < hailstonesSequence(i) Then
            longest = hailstonesSequence(i)
            value = i
        End If
    Next i
    Console.WriteLine(\" longest sequence \"+ longest)
End Sub
Function hailstonesSequence(n As Long) As Long
    Dim a As Long, P As Long
    Dim a1 As Long, a2 As Long, a3 As Long, a4 As Long
    If flag Then Console.WriteLine(\"The sequence \"+ n +\"is \")
    P = 1
    a = n
    If flag Then Console.WriteLine(a)
    While a > 1
        P = P + 1
        If (a Mod 2) = 0 Then
            a = a / 2
        Else
            a = 3 * a + 1
        End If
        If P <= 4 Then If flag Then Console.WriteLine(a)
        a4 = a3
        a3 = a2
        a2 = a1
        a1 = a
    Wend
    If flag Then
        If P <= 4 Then
            Console.WriteLine()
        ElseIf P = 5 Then
            Console.WriteLine(a1)
        ElseIf P = 6 Then
            Console.WriteLine(a2+\" \"+a1)
        ElseIf P = 7 Then
           Console.WriteLine(a3+\" \"+a2 +\" \"+a1)
        ElseIf P = 8 Then
            Console.WriteLine(a4+\" \"+a3\" \"+a2\"\" +a1)
        Else
            Console.WriteLine(\"...\"+ a4 +\" \" +a3 +\" \" +a2 +\" \" +a1)
        End If
    End If
    hailstonesSequence = PEnd Function

-----Sample output--------------------------------

27, 82, 41, 124, ....., 8,4,2,1

Sequence length of 7 is 114