(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
 Gamo Senior Member Posts: 497 Joined: Dec 2016
(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.
--------------------------------------
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
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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
12-27-2018, 07:04 AM (This post was last modified: 12-27-2018 07:45 AM by Gamo.)
Post: #2
 Gamo Senior Member Posts: 497 Joined: Dec 2016
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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