What is the next number in the sequence ___, ____, 16,256, 65,536?

sexiboi150nc

sexiboi150nc

Answered question

2022-10-01

What is the next number in the sequence ___, ____, 16,256, 65,536?

Answer & Explanation

Jeremy Mayo

Jeremy Mayo

Beginner2022-10-02Added 8 answers

More interesting than 2 2 n + 1 :

3 , 5 , 17 , 257 , 65537 , 4294967297 , ...

All such numbers were conjectublack to be prime by Pierre de Fermat.

Unfortunately, no Fermat number beyond 2 2 4 + 1 is known to be prime.

For example, 4294967297 = 641 6700417

It is (in theory) possible to construct a regular ( 2 2 n + 1 ) -sided polygon using ruler and compasses. No other regular polygon with a prime number of sides is constructible using ruler and compasses.
So,
The first two numbers in the sequence are 2 2 0 = 2 and 2 2 1 = 4
The elements of this sequence are 2 2 n for n = 0 , 1 , 2 , ...

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