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(12C Platinum) 3n+1 Conjecture
12-25-2018, 11:55 AM (This post was last modified: 12-25-2018 12:51 PM by Gamo.)
Post: #1
(12C Platinum) 3n+1 Conjecture
This program allows to test the 3n + 1 conjecture.

Consider an integer n.
If it's even, divide it by 2 (n÷2)
If it's odd, multiply by 3 and add 1 (3n + 1)

No matter what value of n, the sequence will always reach 1.
The question is: if we start with an arbitrary integer will we always reach 1?
Nobody knows.
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Procedure:
Positive Integer Number [R/S] display 1
[X<>Y] display Total Iterations
[RCL] 1 display how many time is Odd
[RCL] 2 display how many time is Even
--------------------------------------
Example:

Desire Positive Integer Number is 7

7 [R/S] display 1
[X<>Y] display 16 // Total Iterations
[RCL] 1 display 5 // Odd
[RCL] 2 display 11 // Even
-------------------------------------
Program: FIX 0 (ALG Mode) 38 steps
Code:

STO 0
0
STO 1
STO 2
RCL 0 ÷ 2 = FRAC  
X=0
GTO 022
1
STO+1
RCL 0 x 3 + 1 = 
STO 0
GTO 005
------------------------------
1
STO+2
RCL 0 ÷ 2 = 
STO 0
1
X<>Y
X≤Y 
GTO 034
GTO 005
-----------------------------
RCL 1 + RCL 2 =
RCL 0

***Let's try this on a much faster 12C Platinum Emulator.***

[EEX] 99 [R/S] display 1
[X<>Y] display 567
RCL 1 display 92
RCL 2 display 475

That 92 odds VS 475 even numbers !!!

Gamo
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12-27-2018, 07:04 AM (This post was last modified: 12-27-2018 07:45 AM by Gamo.)
Post: #2
RE: (12C Platinum) 3n+1 Conjecture
This is the updated version that included the Maximum Value as well.

Procedure: (RPN mode)
Mostly the same as previous post but added the Maximum Value.
The maximum value is the highest point then each steps drop down to 1.

n [R/S] display 1
[X<>Y] display Iterations
[RCL] 1 display Odd
[RCL] 2 display Even
[RCL] 3 display Maximum

------------------------------------
Example: FIX 0

7 [R/S] display 1
[X<>Y] display 16 // Iterations
[RCL] 1 display 5 // Odd
[RCL] 2 display 11 // Even
[RCL] 3 display 52 // Max

-------------------------------------
Program: (RPN mode)
Code:

001 STO 0
002  0
003 STO 1
004 STO 2
005  2
006 STO 3   // Initialize 
------------------
007 RCL 0
008  2
009  ÷
010 FRAC
011 X=0    // Test for Even or Odd 
012 GTO 026  // Even start here
013  1    // Odd start here
014 STO+1
015 RCL 0
016  3
017  x
018  1
019  +
020 STO 0
----------------
021 RCL 3
022 X≤Y
023 X<>Y
024 STO 3   // Store Maximum Value
025 GTO 007  // Loop
----------------
026  1
027 STO+2
028 RCL 0
029  2
030  ÷
031 STO 0
032  1
033 X<>Y
034 X≤Y
035 GTO 037   // End Loop
036 GTO 007   // Loop
037 RCL 1  // Odd
038 RCL 2  // Even
039  +    // Total Iterations
040 RCL 0  // Final result is 1

Gamo
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