Collatz Conjecture Calculator | Collatz Conjecture Formula

Last Updated : May 07, 2025

The Collatz Conjecture Calculator just needs intake data from the user to provide the exact & accurate result. So, enter the positive integer as the input value in the below input box of the calculator & click on the calculate button to get the graph and Collatz sequence calculated in no time.

Collatz Conjecture Calculator: Are you feeling that finding a Collatz sequence and obtaining a graph from the given integer is a difficult task? Not anymore, as we have come up with a handy and instant Collatz Sequence Calculator. This tool makes your lengthy calculations so painless and preserves your valuable time to accomplish other calculations too. Also, this handy calculator provides an elaborated solution for you to understand & comprehend the concept for additional math problems.

What is Collatz Conjecture? (Definition)

One of the most famous unsolved problems in mathematics is the Collatz Conjecture, which was introduced by scientist Collatz in 1937. The Collatz mathematical conjecture states that in a sequence, any positive integer term ‘n’ can be calculated from the previous term such that the next term is half the previous term (n/2) if the previous term is even & the next term is calculated by adding one after multiplying the previous term by 3(3n+1).

Collatz Conjecture Formula

The formula for Collatz conjecture is given as function f(n)

f(n) = n/2, if, n is even

f(n) = 3n+1, if, n is odd

Here, ‘n’ is the term in a sequence.

& ‘n’ should always be a positive integer.

What is the (3n+1) Algorithm?

For any positive integer ‘n’, divide it by 2 if it is even or add 1 to it after multiplying by 3 if it is odd. Repeat it for every consecutive term until you get the final answer as 1.

What are the Remarkable Properties of Collatz Conjecture?

The remarkable property of the Collatz conjecture is that whatever is the initial value of ‘n’, the sequence will reach 1 after a finite number of iterations.

If the initial number ‘n’ is odd, then we need more iterations to reach 1.

If the initial number ‘n’ is even, then we need a comparatively less number of iterations to reach 1.

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How to Use Collatz Conjecture Calculator?

Here are the simple steps to use this free calculator and obtain the result.

Enter a positive interger number in the input box of the calculator.
Hit the calculate button.
It will automatically display Collatz Sequence and graph in no time.

Collatz Conjecture Solved Example

Example:

Calculate the sequence of numbers using Collatz conjecture if 1st number in the sequence is 11.

Solution:

Here, the value of n = 11.

Now, we will calculate the Collatz sequence using a table.

We will use formulas of (n/2) or (3n+1) for even & odd numbers respectively.

We will use the Collatz formula & continue the iterations until we get the value as 1.

Steps	number (n)	Even/Odd	Collatz formula	next number
1	11	Odd	f(n) = ((n × 3) + 1) = ((11 × 3) + 1) = (33 + 1) = 34	34
2	34	Even	f(n) = (n / 2) = (34 / 2) = 17	17
3	17	Odd	f(n) = ((n × 3) + 1) n = ((17 × 3) + 1) n = (51 + 1) n = 52	52
4	52	Even	f(n) = (n / 2) n = (52 / 2) n = 26	26
5	26	Even	f(n) = (n / 2) n = (26 / 2) n = 13	13
6	13	Odd	f(n) = ((n × 3) + 1) n = ((13 × 3) + 1) n = (39 + 1) n = 40	40
7	40	Even	f(n) = (n / 2) n = (40 / 2) n = 20	20
8	20	Even	f(n) = (n / 2) n = (20 / 2) n = 10	10
9	10	Even	f(n) = (n / 2) n = (10 / 2) n = 5	5
10	5	Odd	f(n) = ((n × 3) + 1) n = ((5 × 3) + 1) n = (15 + 1) n = 16	16
11	16	Even	f(n) = (n / 2) n = (16 / 2) n = 8	8
12	8	Even	f(n) = (n / 2) n = (8 / 2) n = 4	4
13	4	Even	f(n) = (n / 2) n = (4 / 2) n = 2	2
14	2	Even	f(n) = (n / 2) n = (2 / 2) n = 1	1

FAQ's on Collatz Conjecture 3n+1 Calculator

1. Is there any unsolved math problems?

The Collatz conjecture is considered among the most well-known unsolved problem of mathematics.

2. Is there a prize for solving the Collatz conjecture?

Nobody has succeeded in proving this conjecture, Although the prize for the proof of this problem is 1 million dollars.

3. Why is the Collatz conjecture important?

The Collatz conjecture is a very complex problem in mathematics associated with the oneness of natural numbers when run through a specific function based on being odd or even.

4. Is Collatz conjecture a millennium problem?

Collatz conjecture is not included in Millennium Prize Problems.