Asymptotics about A005228

[A.N.W.Hone at kent.ac.uk]

Hi - 

I think you meant to say g = f ' below. 

I agree it's a hard functional equation to solve...

Andy

> 
>     [2]  f(n) = 1 + SUM(k < n; g(k))
> 
>  
> 
> In order to guess at the asymptotics of f, we handwave f and g 
> into real
> functions and freely translate [1] and [2] into similar real 
> relationships,getting:
> 
>  
> 
>     [3]   f^-1(x) + g^-1(x) = 
> x   where f^-1 is the inverse of f
> 
>  
> 
>     [4]  f = g'
> 
>  
> 
> This leads to
> 
>  
> 
>     [5]  f^-1(x) + (f')^-1(x) = x
> 
>  
> 
> Of course, I have blithely ignored a lot of details, but one 
> might hope that
> a function satisfying [5] would give a good asymptotic to A005228.
> 
>  
> 
> I wish I could solve [5].
> 
> 
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