Collatz Sequence کا حساب کیسے لگائیں
Collatz Sequence کیا ہے؟
The Collatz conjecture states that for any positive integer, repeatedly applying the rule: if even divide by 2, if odd multiply by 3 and add 1 — will always eventually reach 1. It remains one of mathematics' most famous unsolved problems.
فارمولا
If n even: n → n/2; If n odd: n → 3n+1
- n
- positive integer — starting value for the sequence
- s
- stopping time — number of steps to reach 1
مرحلہ وار گائیڈ
- 1If n is even: next = n / 2
- 2If n is odd: next = 3n + 1
- 3Continue until reaching 1
- 4The number of steps is called the "stopping time"
حل شدہ مثالیں
ان پٹ
n = 6
نتیجہ
6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 (8 steps)
ان پٹ
n = 27
نتیجہ
111 steps, reaches maximum of 9,232
اکثر پوچھے جانے والے سوالات
Is the Collatz conjecture proven?
No, it remains one of mathematics' great unsolved problems despite being tested for numbers up to 2⁶⁸.
Why does the Collatz sequence sometimes increase dramatically?
Odd numbers multiply by 3, creating larger values. But many steps follow: divide by 2 repeatedly until odd again.
What is the longest known Collatz stopping time?
For starting values tested, stopping times are in the hundreds. 27 requires 111 steps.
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