Within science, citation counts are widely used to estimate research impact but publication delays mean that they are not useful for recent research. This gap can be filled by Mendeley reader counts, which are valuable early impact indicators for academic articles because they appear before citations and correlate strongly with them. Nevertheless, it is not known how Mendeley readership counts accumulate within the year of publication, and so it is unclear how soon they can be used. In response, this paper reports a longitudinal weekly study of the Mendeley readers of articles in 6 library and information science journals from 2016. The results suggest that Mendeley readers accrue from when articles are first available online and continue to steadily build. For journals with large publication delays, articles can already have substantial numbers of readers by their publication date. Thus, Mendeley reader counts may even be useful as early impact indicators for articles before they have been officially published in a journal issue. If field normalized indicators are needed, then these can be generated when journal issues are published using the online first date.