# [seqfan] Arc-Tangent Irreducible Rationals

pauldhanna at juno.com pauldhanna at juno.com
Thu Jun 5 23:43:25 CEST 2003

```This is a sequence that seems rather fundamental, yet I can not find it on the OEIS:

(*) the arc-tangent irreducible rationals.

This sequence is to involve all positive reduced fractions.

Suppose we let this sequence (*) be represented by a table of
integers that is to be constructed in the following manner.

The first row of the table (*) lists 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,...}

The n-th row lists the denominators of the reduced fractions that
have the form n/T(n,k), gcd(n,T(n,k))=1, such that:

arc-tangent( n/T(n,k) ) is not the sum or difference of the
arc-tangents of any two fractions with numerators <= n;

when one of these two fraction addends have a numerator = n,
consider the fraction addend only when the denominator < T(n,k).

What is the resulting table?

Thanks for any references, suggestions, or solutions,
Paul

```