[seqfan] Re: rational sequence $$ f_n= (\frac{n}{f_{n-1}}+1)(n+1) \; , f_0 = 1 $$

Paul Barry PBARRY at wit.ie
Thu Mar 26 16:00:17 CET 2009

Denominators appear to be Fibonacci numbers or divisors of Fibonacci numbers.

Best wishes,
Paul Barry.

>>> Georgi Guninski <guninski at guninski.com> 26/03/2009 12:57 >>>
rational sequence:
$$ f_n= (\frac{n}{f_{n-1}}+1)(n+1) \; , f_0 = 1 $$

f[n]= (n / f[n-1]+1)*(n+1) , f[0]=1

is something known about this sequence?

i found possible doubling formulas for this so it seems efficiently

1. period mod p is uninteresting to me
2. i suspect it may be a combination of exponential and rational
functions, though Fricas (a fork of Axiom) can't find such.
3. can't find relations for the numerators or denominators and OEIS
returns nil.




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