Test if a number is fibonacci

Question

I know how to make the list of the Fibonacci numbers, but i don\'t know how can i test if a given number belongs to the fibonacci list - one way that comes in mind is genera

Answer 1

Positive integer ω is a Fibonacci number

If and only if one of 5ω² + 4 and 5ω² - 4 is a perfect square

from The (Fabulous) FIBONACCI Numbers by Alfred Posamentier and Ingmar Lehmann

bool isFibonacci(int  w)
{
       double X1 = 5 * Math.Pow(w, 2) + 4;
       double X2 = 5 * Math.Pow(w, 2) - 4;

       long X1_sqrt = (long)Math.Sqrt(X1);
       long X2_sqrt = (long)Math.Sqrt(X2);   

       return (X1_sqrt*X1_sqrt == X1) || (X2_sqrt*X2_sqrt == X2) ;
}

I copied it from this source

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Snippet that prints Fibonacci numbers between 1k and 10k.

for (int i = 1000; i < 10000; i++)
{
         if (isFibonacci(i))
              Console.Write(" "+i);
}

OMG There are only FOUR!!!

With other method

from math import *

phi = 1.61803399
sqrt5 = sqrt(5)

def F(n):
    return int((phi**n - (1-phi)**n) /sqrt5)

def isFibonacci(z):
    return F(int(floor(log(sqrt5*z,phi)+0.5))) == z

print [i for i in range(1000,10000) if isFibonacci(i)]