Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

There is known Catalan sequence :

$C_n=2^{C_{n-1}}-1$ , with $C_0=2$

I have noticed that following sequence produces prime numbers for the first four terms (I don't know if the fifth term is a prime number or not) :

$P_n=2^{P_{n-1}}-3$ , with $P_0=3$

Are there some similar prime number sequences of the form : $P_n=2^{P_{n-1}}-a$ ?

share|cite|improve this question

1 Answer 1

In short, no. This is because there is no known $a$ such that we can prove $2^n -a$ will be prime infinitely often.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.