For general use, use this calculator:

Cycles: Enter a number to test first

Numbers: Enter a number to test first

This 3n + 1 calculator, although not very fast, provides interesting visualizations on the cycles that the integer you chose to simulate is going through. At the end, it provides you with the peak height and amount of cycles.

You can use the 3n + 1 calculator and visualization here.

Alternatively, you can use this python code to calculate 3n + 1 really fast:

testNum = input('What integer would you like to calculate?')
testNum =  int(testNum)
original = testNum
cycles = 0
peak = 0
while testNum != 1.0:
    if testNum % 2  == 0:
        testNum = testNum/2
    else:
        testNum = testNum * 3 + 1
        if testNum > peak:
            peak = testNum
    cycles = cycles + 1
print('Cycles: ' + str(cycles))
print('Peak: ' + str(peak))
print('Test number: ' + str(original))copy

What is 3n + 1?

3n+1 is an unsolved mathematical problem created in 1937. It states that if a number is odd, it is multiplied by three and increased by one, and if it is even, it is divided by two. Currently, no integer has been found that can go through these two rules without eventually getting stuck at 1. This is a fun little problem you can experiment around with on our calculator and visualization page, providing more accurate and quicker visualizations.

3n + 1 Examples

3n + 1 can be graphed, like so:

The graph contains all of the numbers 9 will hit before it goes down to 1.

Works Cited

Wikipedia contributors. “Collatz Conjecture.” Wikipedia, 19 Dec. 2023, en.wikipedia.org/wiki/Collatz_conjecture.