[seqfan] Arc-Tangent Irreducible Rationals

[Paul D Hanna]

Apologize for the prior e-mail; after a little more tinkering, 
I see that the reciprocal of the Stormer numbers do indeed 
form the 'arc-tangent irreducible rationals'.  
There are no others.  This was not as obvious to me 
as it probably is to most of you.

The Stormer numbers are now very interesting to me,
because the entire set of arc-tangents of the rationals 
can then be expressed as sums of +-arctan(1/A005528(n)).
This implies that the Stormer numbers are related to 
the Gaussian integers.

Does anyone know of a more direct formula for the
n-th Stormer number than that given in A005528?

Thank you,
        Paul

On Thu, 5 Jun 2003 21:43:25 GMT pauldhanna at juno.com writes:
> 
> This is a sequence that seems rather fundamental, yet I can not find 
> it on the OEIS:
> 
> (*) the arc-tangent irreducible rationals.
> 
> ... the denominators of 
> unit fractions that are arc-tangent irreducible; these are 
> the Stormer numbers (see A005528):
>    T(1,k)={1,2,4,5,6,9,10,11,12,14,15,16,19,20,22,23,24,25,26,...}
>