Hi, I think that I discovered a new sequence related to Fibonacci sequence:
You might knew that the Fibonacci sequence starts with 0 and 1 and the following number is the sum of the previous 2; every time you go further in the sequence, the ratio of two consecutive numbers be nearer to the golden ratio (phi). But you can start with any two numbers not only 0 and 1 for example (2, 6; 490, 10; 56, 56...etc.) or two similar numbers and the ratio of two consecutive numbers is also the golden ratio. If we think deeper, we can start with phi and phi as the first two numbers and the ratio of two consecutive numbers (if you choose them far away from the beginning) is also approximately phi. But if you look on the numbers of this sequence, an amazing pattern appear. The first 4 or 5 numbers are ordinary but the 5th or 6th numbers are the beginning of the pattern. The digits after the decimal point of these numbers is as following:
0,9,0,9,0,99,00,99,00,99,000,999,000… and so on!!!