The Collatz conjecture

Maths

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A sequence is defined as follows: Start with any positive integer value (𝑛). Each term is found from the previous term as follows: If the value is even, divide it by 2 (𝑛/2). If the value is odd, multiply it by 3 and add 1 (3𝑛+1).

If the first term of the sequence is 30, what would the second term be?

If the second term of the sequence is 30, what would could the first term be?

Fill in the gap: The Collatz conjecture states: no matter the start number (𝑛), the sequence will always reach __________.

In what year did Collatz make his conjecture?

Fill the gap: Every even integer greater than two can be written as the sum of two __________ integers.

Goldbach wrote his conjecture in a letter. Who was the letter to?

True or false: Goldbach's conjecture is proven to be true.

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