  In this paper, we apply experimental number theory to two integrable quantum
models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi
gas with contact interactions. We identify patterns in weak- and
strong-coupling series expansions of the ground-state energy, local correlation
functions and pressure. Based on the most accurate data available in the
literature, we make a few conjectures about their mathematical structure and
extrapolate to higher orders.
