Collatz Sequence ની ગણતરી કેવી રીતે કરવી
Collatz Sequence શું છે?
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.
સૂત્ર
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
પગલું દ્વારા પગલું માર્ગદર્શિકા
- 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"
Worked Examples
ઇનપુટ
n = 6
પરિણામ
6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 (8 steps)
ઇનપુટ
n = 27
પરિણામ
111 steps, reaches maximum of 9,232
Frequently Asked Questions
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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