  In this note, we explore two families of sequences associated to a suitable
integer sequence: the gap-sum sequence and the gap-product sequence. These are
the sums and the products of consecutive numbers not in the original sequence.
We give closed forms for both, in terms of the original sequence, and in the
case of Horadam sequences, we find the generating function of the gap-sum
sequence. For some elementary sequences, we indicate that the gap-product
sequences are given by the Fuss-Catalan-Raney numbers.
