The f-index is proposed here as a new citation index to be created in addition to the h-index and i10-index. The f-index (by definition) would simply only count all publication citations for which an individual author or scientist is listed as the first author. A key advantage of the f-index would be that it would provide an indicator of an author's productivity in terms of being the primary contributor responsible for actually writing the predominant major portion of a publication (for which the first-author status is justified). Many other advantages are possible. Multiple citation indices are useful for different author metrics. Other related indices could be created for other purposes such as, for example, a comparable f10-index or fh-index that may actually be more useful. Any feedback or comments would be appreciated.