What are the next few numbers in the following sequence?

0.1, 0.2, 0.4, 0.7, 1.2, 2.0, 2.13, 2.34, 2.68, 3.23, 4.12, 4.264, ...

Note: the original problem erroneously listed the last term of the sequence as 4.263 - this has been fixed

Yes, I assume it's a series where the difference terms are Fibonacci numbers, except put a decimal point in front of each Fibonacci number.

I plotted out about 250 terms of this sequence and plotted F(n) vs n.  It turns out to be very close to a linear relationship:
F(n) =~ 0.39 n + errorterm   Where the errorterm is cyclic, and looks like the sum of several cycles of different periods, including a dominant cycle of period 4.  A Fourier analysis of the errorterm might be interesting.

Is there anything inherent in the Fibonacci sequence that has a period of every 4th term?  It might just be due to the number of terms it takes for the sequence to grow another order of magnitude, so you have to divide by another factor of 10 to get the decimal point in the right place.

Posted by Larry on 2005-06-01 04:42:05