Starting with any positive integer N, we define the Collatz sequence corresponding to N as the numbers formed by the following operations:
N → N/2 ( if N is even)
N → 3N + 1 (if N is odd)
i.e. If N is even, divide it by 2 to get N / 2. If N is odd, multiply it by 3 and add 1 to obtain 3N + 1.It is conjectured but not yet proven that no matter which positive integer we start with; we always end up with 1.
For example, 10 → 5 → 16 → 8 → 4 → 2 → 1
Note: The sequence should end at the 1st occurence of integer 1.
The length of the Collatz sequence for some given N is defined as the number of numbers in the sequence starting with N and ending at 1.Given a positive integer N, the task is to print the maximum Collatz sequence length among all numbers from 1 to N (both included).
The first line of input contains a single integer T denoting the number of test cases. Then T test cases follow. Each test case consists of a single line containing a positive integer N.
Corresponding to each test case, in a new line, print the maximum Collatz sequence length among all numbers from 1 to N (both included).
1 ≤ T ≤ 100
1 ≤ N ≤ 106
For the 1st test case where N = 3
For N= 3 we need to check sequence length when sequence starts with 1,2, and 3.
when sequence starts with 1, it's : 1 length = 1
when sequence starts with 2, it's : 2->1, length = 2
when sequence starts with 3, it's : 3->10->5->16->8->4->2->1, length = 8, which is max of all.
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