Fibonacci

[Dean Hickerson]

Emeric Deutsch wrote:

> Hello Yasutoshi,
> Here are the first 11 terms of your first sequence:
> 2, 3, 7, 23, 103, 613, 4751, 47137, 582511, 8758339, 156819893
> I have used Maple.
> First I wrote a program to get InversePrime (not necessarily the
> best):
> ip:=proc(n) local P, i: P:={}: if isprime(n)=true then for i from 2 to n
> do if isprime(i)=true then P:=P union {i} else P:=P fi: od: nops(P) else X
> fi: end;
>
> Then sequence is given by
>
> a:=proc(n) if n=1 then 2 elif n=2 then 3 else ithprime(ip(a(n-2))+a(n-1))
> fi end; seq(a(n),n=1..9);

Am I missing something?  Isn't InversePrime(n) just the number of primes
<= n, which is called pi(n) by number theorists and by Maple?

If so, you don't need both ithprime(i) and pi(n) to do the calculation.
Instead, let a(n) be the b(n)'th prime, and use

    a(n) = ithprime(b(n))

    b(n) = b(n-2) + a(n-1)

In my opinion, this is one of those artificial sequences that just
clutters up the database, so I'm not going to provide any additional terms.

Dean Hickerson
dean at math.ucdavis.edu