This work presents some instances of Experimental Mathematics in Number Theory. The arithmetical properties of an arctangent sum is explored, in particular, its connections to different mathematical objects are shown. One of this connections is the link between the sum and a sequence of type tn=Pnt n-1, 0.0.1 where P(x) is a polynomial with integer coefficients. These type of sequences arise in different types of problems like the integration of rational functions and the evaluation of infinite sums The asymptotic behavior of the p-adic valuation for sequences of type (0.0.1) is described. In particular, the connection between the zeros of the polynomials P(x) in the finite field Z/pZ and the growth of the p-adic valuation is presented Finally, in the last chapter a relation between Dirichlet Series and the evaluation of a class of logarithmic integrals is studied
