Project Euler Forum

I'm working on the bonus problem about negatively continued fractions, does the set of coefficients have to repeat immediately or can there be a non-repeating section first?

Periodic negatively continued fractions have no non-repeating section.

Great thanks. This is a hard question, there seems to be very little written about negatively continued fractions so it's hard to learn the number theory for it. My code gives the wrong answer and only takes 13 hours

Another question, it's not clear to me if repeated sequences are valid, for example if 1,2 is a complex sequence, and 1,2,1,2 is also complex, then do we count both? Because by my calculations, 1,1 is a complex sequence but in the example it says that the only complex sequences that are 2 elements long are 1,2 2,1 1,3 and 3,1.

hughbert_cumberdale wrote: Mon Jun 01, 2026 11:50 pm Another question, it's not clear to me if repeated sequences are valid, for example if 1,2 is a complex sequence, and 1,2,1,2 is also complex, then do we count both?

They are infinite periodic sequences, so $\overline{1, 2}$ and $\overline{1, 2, 1, 2}$ are the same sequence and should only be counted once.