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<DIV><FONT face="MS UI Gothic" size=2> I thank seqfans
who commented about my mail "Fibonacci".<BR> I have
few knowledge of standard representation in mathematics.<BR>
Because all books of mathematics which I have are in Japanese.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> Before I posted the
mails, I learned about the word "inverse function" on
MathWorld.<BR> 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".</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> [definition of
InversePrime(n)] <BR> Don't read it {InversePrime}(n).
"InversePrime" sounds strange, I want to know what it is. <BR>
But read it "Inverse function of Prime(n)". <BR> 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).</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> [definition of
InverseFibonacci(n)]<BR> It is the same thing as
InversePrime(n). It is the "inverse function of
Fibonacci(n)".<BR> Fibonacci(n) means the following function
f(n). So, InverseFibonacci(n) means {number of Fibonacci numbers
<=n}<BR> f(n)=f(n-1)+f(n-2),
f(1)=1, f(2)=2 <BR> <BR> I rewrote
the definition.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> %N A000001 If a(n-2) is
i-th Fibnacci number
then<BR>
a(n)=Fibonacci(i+a(n-1)), a(1)=1,
a(2)=2.<BR>
Where Fibonacci(n) means the following function f(n)</FONT></DIV>
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<DIV><FONT face="MS UI Gothic" size=2>
<DIV><FONT face="MS UI Gothic" size=2>
<DIV><FONT face="MS UI Gothic"
size=2>
f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2 </FONT></DIV>
<DIV> %e A000001 a(5)=Fibonacci(3+8)=144.</DIV>
<DIV>
<DIV> Because
a(3) is third Fibonacci number and a(4)=8 </DIV> </DIV>
<DIV> Yasutoshi</DIV>
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