Xiaoming loved music since he was a child, so his father enrolled him in a piano interest class when he was 7 years old. Xiaoming persisted in studying and studied for more than seven years in a blink of an eye.

With Xiaoming's rich knowledge of mathematics, his father, as a university mathematics teacher, intends to test his son: "Xiaoming, you have studied mathematics and piano since childhood. Did you find that there is also mathematical knowledge hidden on the piano keyboard? " "Xiaoming was confused by his father:" I only know that the beat on the score is expressed by fractions, and the notation can also be written in Arabic numerals. But what does this piano keyboard have to do with mathematics? "Dad intends to guide his son:" You see, on the piano keyboard, from one key C to the next key C is an octave in music, as you all know. * * * contains the key 13, with 8 white keys and 5 black keys. Five black keys are divided into two groups, one with 2 black keys and the other with 3 black keys, 2, 3, 5, 8 and 13. Have you found any rules to follow? "Xiao Ming thought for a long time but didn't want to come out. Is there really any wonderful law in this series of numbers? In fact, after careful observation, we can easily find that the numbers 2, 3, 5, 8 and 13 on the piano keyboard are regular. This series begins with the third item, each item is equal to the sum of the first two items. For example, 5=2+3, 8 = 5+3 and so on. Don't underestimate this seemingly ordinary series, which is the first few numbers in the famous Fibonacci series. The general formula is fn =1+5 ÷ 5n-1-5 ÷ 2n ÷ 5 (also called "Binet.Alfred formula", which is an example of using irrational numbers to represent rational numbers). Interestingly, such a series of completely natural numbers are actually represented by irrational numbers.