Question

Assuming I’m asked to generate Fibonacci numbers up to N, how many numbers will I generate? I’m looking for the count of Fibonacci numbers up to N, not the Nth number.

So, as an example, if I generate Fibonacci numbers up to 25, I will generate:

• 1, 1, 2, 3, 5, 8, 13, 21
• that’s 8 numbers

How do I calculate this mathematically for an arbitrary “n”?

Answer 1

You can use the following formula (see here):

n(F) = Floor(Log(F * Sqrt(5) + 1/2) / Log(Phi))