In a recent work, the authors provided the first-ever characterization of the values modulo where is the number of (unrestricted) -ary partitions of the integer and is a fixed integer. That characterization proved to be quite elegant and relied only on the base representation of . Since then, the authors have been motivated to consider a specific restricted -ary partition function, namely , the number of -ary partitions of where there are no “gaps” in the parts. (That is to say, if is a part in a partition counted by , and is a positive integer, then must also be a part in the partition.) Using tools similar to those utilized in the aforementioned work on , we prove the first-ever characterization of modulo . As with the work related to modulo , this characterization of modulo is also based solely on the base representation of .