Collatz who? #3

Computer Science Level 3

The Collatz Procedure is $f=\text{If}\left[\text{EvenQ}[\text{\#1}],\frac{\text{\#1}}{2},3 \, \text{\#1}+1\right]\&$ or, in other words, one application of the procedure is if the number is even, then the result is division of the number by 2, otherwise the result of the procedure is multiply the number by 3 and then add 1 to the product. The procedure is normally applied to positive integers. In this problem, the procedure will only be applied to positive integers. Usually, if the procedure is applied to the previous result repetitively, then a 4-2-1 cycle will be reached. It is conceivable that some other cycle might be reached or the numbers will never reach a cycle of some sort.

This problem's question: For the starting integers from 1 to 99, including the starting integer and the 4-2-1 that ends the procedure, what is the highest integer reached by any starting integer? Enter your answer as 100*(the highest value reached)+(the starting integer).

Note: This is a computation problem. A computer solution is acceptable.

Clarification: the sequence starting integer in the answer should the minimum integer to reach the maximum.

The answer is 923227.

2 solutions

Fletcher Mattox
Aug 11, 2019

While 27 is the first integer less than 100 which yields a maximum of 9232, there are many others. What is special about 27? I found these, too.

   [27,31,41,47,54,55,62,63,71,73,82,83,91,94,95,97]

Since the starting integer is encoded into the answer, I got it wrong. Am I missing something?

My mistake for not making it clear that it should be the minimum integer that achieves 9232.

A Former Brilliant Member - 1 year, 10 months ago

A Former Brilliant Member
Mar 10, 2019

27, {27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1}

$\max (\text{Flatten}[\text{Table}[\{i,\text{NestWhileList}[f,i,\text{\$\#\$1}\neq 1\&]\},\{i,99\}]]) \Longrightarrow 9232$

$100\times 9232+27 \Longrightarrow 923227$

Collatz who? #3

The answer is 923227.

2 solutions

1 pending report

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