Mersenne and Mandelbrot Sequences

The video explores the arithmetic of dynamical sequences, starting with the Mersenne sequence and its prime divisors. It discusses the generation of sequences using linear and nonlinear functions, including the impact of negative numbers and fractions. The video also touches on the Mandelbrot set's influence on sequence properties, highlighting the unique behavior of certain fractions within this set.

What is the function used to generate the Mersenne sequence in the video?

• f(x) = 2x + 1

• f(x) = x^2 + 1

• f(x) = 3x + 2

• f(x) = x^2 - 1

What is the main question about the Mersenne sequence discussed in the video?

• Are there infinitely many prime numbers in the sequence?

• Do all numbers in the sequence have the same prime divisor?

• Are all numbers in the sequence even?

• Is the sequence finite?

What happens at the sixth element of the Mersenne sequence?

• It is not divisible by any prime number.

• It repeats a previous prime divisor.

• It introduces a new prime divisor.

• It is the largest number in the sequence.

What is the function used to generate a sequence with x squared plus 1?

• f(x) = x^2 + 1

• f(x) = 2x + 1

• f(x) = x^2 - 1

• f(x) = 3x + 2

In the sequence generated by x squared plus 1, what is true about the numbers after 2?

• They are all prime numbers.

• They all have a new prime divisor.

• They are all multiples of 3.

• They are all even.

What happens when negative numbers are used in the sequence generation?

• The sequence has no new prime divisors.

• The sequence becomes infinite with new prime divisors.

• The sequence repeats itself.

• The sequence becomes finite.

What is the exception when using fractions in sequence generation?

• Fractions always result in new prime divisors.

• Fractions never result in new prime divisors.

• Some fractions may not result in new prime divisors.

• Fractions result in repeating sequences.

What is the Mandelbrot set related to in the video?

• The finiteness of sequences.

• The repetition of sequences.

• The generation of even numbers.

• The occurrence of new prime divisors in sequences.

Where must a number lie to potentially disrupt the sequence of new prime divisors?

• In the set of even numbers.

• Outside the Mandelbrot set.

• Inside the Mandelbrot set.

• On the real number line.

What is the significance of the number minus 7 over 4 in the video?

• It is a prime number.

• It is the only known fraction that disrupts the sequence.

• It is a repeating number in the sequence.

• It is outside the Mandelbrot set.