primes in A000009 and A000081

[David Broadhurst]

Eric W. Weisstein:
> ( A000009[ n ] is prime )
> 5, 7, 22, 70, 100, 495, 1247, 2072, 320397

Dean Hickerson:
> I'd expect there to be infinitely many primes of this type.

I looked at ( A000081[ n ] is prime )
i.e. n such that there is a prime number of rooted trees with n nodes.
The sequence seems to begin

           3, 10, 15, 343, 387, 1087         (*)

in line with my probabilistic guess of log(N)/log(c) elements with
n < N, where c=2.95576528... is the Otter constant noted by

Christian Bower:
> http://www.mathsoft.com/asolve/constant/otter/otter.html

The next member of (*) might be rather hard to find.

David Broadhurst