Fibonacci

[kohmoto]

    I thank seqfans who commented about my mail "Fibonacci".
    I have few knowledge of standard representation in mathematics.
    Because all books of mathematics which I have are in Japanese.

    Before I posted the mails, I learned about the word  "inverse function" 
on MathWorld.
    On the page, "inverse sin"  " inverse cos" are described, so I supposed 
that for all functions f, mathematicians call the inverse functions of them 
" inverse f".

    [definition of InversePrime(n)]
    Don't read it  {InversePrime}(n). "InversePrime" sounds strange, I want 
to know what it is.
    But read it "Inverse function of Prime(n)".
    Where Prime(n) means n-th prime. So, InversePrime(n) means {number of 
primes <=n}. If n=i-th prime then it gives i. In other word it is pi(n).

    [definition of InverseFibonacci(n)]
    It is the same thing as InversePrime(n). It is the "inverse function of 
Fibonacci(n)".
    Fibonacci(n) means the following function f(n). So, InverseFibonacci(n) 
means {number of Fibonacci numbers <=n}
         f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2

    I rewrote the definition.
    %N A000001 If a(n-2) is i-th Fibnacci number then
                     a(n)=Fibonacci(i+a(n-1)), a(1)=1, a(2)=2.
                     Where Fibonacci(n) means the following function f(n)
                     f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2
    %e A000001 a(5)=Fibonacci(3+8)=144.
                      Because a(3) is third Fibonacci number and a(4)=8

    Yasutoshi
 
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