Collatz conjecture

Hello everyone!

The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. Otherwise, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.

I am trying to program something that will show me the amount of steps (of loops) that happened before the number n became smaller than the initial number.
It is the variable dva, but I don't know how to find it!
then I also need to show every step: every value of n (one or each loop) and
Also the highest value that n takes throughout the loops (am)
and the number of steps until n reaches 1 (dv)

I have started something but I feel stuck moving forward as the beginning doesn't even work..

can someone point me to where I'm messing up here?

Sub collatz2()
n = InputBox("type in a number ")

am = 0

Do While n <> 1
    If n Mod 2 = 0 Then
        n = n * 2
    Else: n = n * 3 = 1
    End If

If n > am Then
    Z = am
End If

x = x + 1
Dim ligne As Integer
'Cells(1, 1).Value = "Trip"
Cells(x, 1).Value = n

Loop

'Cells(1, 2).Value = "Steps"
Cells(x, 2).Value = x

'Cells(1, 3).Value = "Maximal altitude"
Cells(x, 3).Value = am

End Sub

Is this what you want?

Sub collatz2()
n = InputBox("type in a number ")

am = 0

Do While n <> 1
    If n Mod 2 = 0 Then
        n = n / 2
    Else
        n = n * 3 - 1
    End If

If n > am Then
    Z = am
End If

x = x + 1
Dim ligne As Integer
'Cells(1, 1).Value = "Trip"
Cells(x, 1).Value = n

Loop

'Cells(1, 2).Value = "Steps"
Cells(x, 2).Value = x

'Cells(1, 3).Value = "Maximal altitude"
Cells(x, 3).Value = am

End Sub

Is it required the solution be VBA? If not here is formula approach.

	A	B	C	D	E	F
1	Row #s	+ Integer	n < 17 (dva)	am	loops till 'dv'
2	1	17	4	52	13	In B3 and down: =ISEVEN(B2)*B2*0.5+ISODD(B2)*(B2*3+1)
3	2	52				In C2: =MATCH(1,INDEX(--($B$2:$B$22<B2),0),0)
4	3	26				In D2: =MAX(B:B)
5	4	13				In E2: =MATCH(1,$B$2:$B$22,0)
6	5	40
7	6	20
8	7	10
9	8	5
10	9	16
11	10	8
12	11	4
13	12	2
14	13	1
15	14	4
16	15	2
17	16	1
18	17	4
19	18	2
20	19	1
21	20	4
22	21	2
23

Let's start with this.
Startvalue goes in C2 then push button.

There's nothing wrong with that. It reflects the total number of times value goes under startingvalue.

Hi Rudi,

I added another long variable and altered your loop to ending procedure:

'The basic logic behind the process here.
Do While intResult <> 1
    
    If intResult Mod 2 > 0 Then
'If number is even
    intResult = (intResult * 3) + 1
    c = c + 1
Else
'If number is odd
    intResult = intResult / 2
    c = c + 1
End If
    If intResult < intSeed Then _
    z = z + 1: k = IIf(k = 0, c, k)
    
'display loop results
Range("A" & startRow) = intCount: Range("B" & startRow) = intResult
startRow = startRow + 1: intCount = intCount + 1

Loop

'display summary
Range("D2") = c
Range("E2") = z
Range("F2") = k - 1

It doesn't accumulate the altitude maximale but this works:

Sub collatzCandicee()


Dim startRow As Double, duree As Double, x As Double

Dim n As Double, ev As Long, z As Long, am As Long


'On vide le classeur
Range("A2:B" & Rows.Count).Value = vbNullString

n = InputBox("Entrez un nombre entier")
'On donne pour valeur initiale à n le nombre donné par l'utilisateur
x = n

startRow = 2
duree = 1 'C'est le début du décompte du nombre d'étapes avant d'obtenir 1
Range("C2").Value = x
Range("C1").Value = "Nombre de départ"
am = 0
z = 0
    
'On crée une boucle qui fonctionne tant que n n'a pas atteint 0
Do While n <> 1
    
    If n Mod 2 > 0 Then
'Si le nombre est pair
n = (n * 3) + 1
    ev = ev + 1
Else
'Si le nombre est impair
    n = n / 2
    ev = ev + 1
End If

If x > n Then
    dva = IIf(dva = 0, ev, dva)
End If


'If n > x And am = duree Then
'dva = dva + 1
'End If
'Range("F1").Value = "durée du vol en altitude"
'Range("F2") = dva




'On fait apparaitre la valeur à chaque boucle
Range("A" & startRow) = duree: Range("B" & startRow) = n
startRow = startRow + 1: duree = duree + 1

'If WorksheetFunction.Max(x, n) > am Then
'am = WorksheetFunction.Max(x, n)
'End If

Loop



'On affiche les réponses
Range("D1").Value = "Durée du vol"
Range("D2") = ev
Range("E1").Value = "Durée du vol en altitude"
Range("E2") = dva
Range("F1").Value = "Altitude maximale"
Range("F2") = am



End Sub

You're welcome!

I think this covers it all.

Sub collatzCandicee()

Dim startRow As Double, duree As Double, x As Double
Dim n As Double, ev As Long, z As Long, am As Long
'On vide le classeur
Range("A2:B" & Rows.Count).Value = vbNullString
n = Application.InputBox("Insert startnumber", , , , , , , 1)
'On donne pour valeur initiale à n le nombre donné par l'utilisateur
x = n
flag = False: am = 0
startRow = 2
duree = 1 'C'est le début du décompte du nombre d'étapes avant d'obtenir 1
Range("C2").Value = x
Range("C1").Value = "Nombre de départ"
am = 0: z = 0
'On crée une boucle qui fonctionne tant que n n'a pas atteint 0
Do While n <> 1
    If n Mod 2 > 0 Then
'Si le nombre est pair
        n = (n * 3) + 1
        ev = ev + 1
        If flag = False Then: If n > am Then am = n
    Else
'Si le nombre est impair
        n = n / 2
        ev = ev + 1
        If flag = False Then: If n > am Then am = n
    End If
    If x > n Then
        dva = IIf(dva = 0, ev, dva)
        flag = True
    End If
'On fait apparaitre la valeur à chaque boucle
    Range("A" & startRow) = duree: Range("B" & startRow) = n
    startRow = startRow + 1: duree = duree + 1
Loop
'On affiche les réponses
Range("D1").Value = "Durée du vol"
Range("D2") = ev
Range("E1").Value = "Durée du vol en altitude"
Range("E2") = dva
Range("F1").Value = "Altitude maximale"
Range("F2") = am
End Sub