Discrete Math: Please don\'t repost previous responses. Choose any positive inte

Question

Discrete Math: Please don't repost previous responses. Choose any positive integer. Powers of two here are not very interesting, so choose something else.

If the number you have chosen is even, divide it by two. If it's odd, multiply it by three and add one.

Now, with the result, repeat the same process. If the number is even divide it by two. If it's odd multiply it by three and add one. Keep repeating this process on the outcome. You will generate (*recursively*) a sequence of positive integers.

Present your sequence so others can compare it with their own. It would be useful to answer this part early in the week. That way others can use your data to help answer (2).What do you observe? Make a (wild) conjecture based on your observation.Try a different starting number and see if the same thing happens.[Optional] Experiment further. Try starting with a negative number. Try a slightly different sequence.[Optional] How *might* you start to prove your conjecture. (n.b. a proof is not needed here).

Explanation / Answer

Let us choose 5

Now as 5 is odd, so we need to multiply by 3 and add 1 to it, so we will get (5*3)+1 = 15+1 = 16

Now since 16 is even, divide by 2, thus leaving us with 8

Now since 8 is even, divide by 2, thus leaving us with 4

Now since 4 is even, divide by 2, thus leaving us with 2

Now since 2 is even, divide by 2, thus leaving us with 1

Thus series formed would be 5, 16, 8, 4, 2, 1

Observation : Once you get a number which is of the form 2^n where n is a natural number you will start getting other term of series as that number divided by 2. Else the random number series will keep on generating with next term greater or smaller than previous term

Now if we take a negative number -9

Now since -9 is odd, multiply by 3 and add 1, thus leaving us with (-9*3)+1 = -26

Now since -26 is even, divide by 2, thus leaving us with -13

Now since -13 is odd, multiply by 3 and add 1, thus leaving us with (-13*3)+1 = -38

Now since -38 is even, divide by 2, thus leaving us with -19

Series thus formed is -9, -26, -13, -38, -19

Observation : A random series is formed with next term either greater or lesser than previous term

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.