### Integer values of recurrences

Victor Moll writes:

*“The recurrence comes from a simple finite sum of values of the arctangent function. Starting at you will see that . We have conjectured that this never happens again. The paper “*Arithmetical properties of a sequence arising from an arctangent sum*” (see below) contains some dynamical systems that needs to be explored.”*

The aim of his project is to explore this conjecture computationally. In particular, what is the behavior of the sequence of fractional parts of the defined in the Amdeberhan *et al* (2007) article?

A plot of shows two values of for which is small, namely :

However, a check reveals that and .A plot of reveals spots, increasingly rare, where :

### References & readings

- Tewodros Amdeberhan, Luis A. Medina & Victor H. Moll(2007) Arithmetical properties of a sequence arising from an arctangent sum. J. Number Theory (2007)(arithmetical _ properties _ of _a_ sequence _ arising _ from _ an _ arctangent _ sum)