HP 25 Fibonacci sequence in one program step

[Albert Chan]

(10-14-2021 10:03 AM)C.Ret Wrote:  

We can use this to get fib(n+m) = fib(m)*fib(n+1) + fib(m-1)*fib(n)

If n=m, we have fib(2n) = fib(n) * (fib(n+1) + fib(n-1))
Using this, we can can 1/sqrt(5) another way

φ^n ≈ fib(2n) / fib(n) = fib(n+1) + fib(n-1) ≈ fib(n) * (φ+1/φ) = fib(n) * √5

fib(n) = round(φ^n / √5)