While working on some problem or just playing around (with numbers) you could discover something by accident. Noticing the Collatz conjecture for only two numbe

While working on some problem or just playing around (with numbers) you could discover something by accident. Noticing the Collatz conjecture for only two numbers is probably enough to cause some curiosity and then you try some more examples and not much later you have a conjecture without any idea why it could be true.