A097417 and related

[Benoit Cloitre]

There are related seq such as :

A038044 which satisfies (new comments) :
*********************************************************************
%F A038044 a(1)=1 a(n+1)=sum(d|n, a(d)*a(n/d))
%F A038044 a(prime(k)+1)=2*a(prime(k))
%F A038044 a(n) is asymptotic to c*2^n where c=0.353030198...
*********************************************************************

A078346  which  satisfies (new comment) :
*********************************************************************
%F A078346 k>1 a(prime(k)+1)=2*a(prime(k))-a(prime(k)-1)+1
*********************************************************************

I found no simple asymptotic formula for A078346 since x^2-2x+1=(x-1)^2 
and there is no root >1. I guess limit log(a(n))/log(n)^2 exists.

Benoit

> A097417
>
> the sequence satisfy the "partial linear recursion" :
>
> a(prime(n)+1) = 3*a(prime(n))- a(prime(n)-1)

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