Continuous measurements of intermediate air ion size distributions were carried out in the small town Tartu, Estonia, from 1 April 2010 through 7 November 2011. The intermediate ions are charged aerosol particles of diameter 1.5-7.5 nm. In this paper we study what information about neutral nanoparticles of atmospheric aerosols can be drawn from the air ion measurements. Rough estimates of the growth rate and the size distribution of neutral nanoparticles were derived for the subset of measurements while the concentration of the intermediate ions was close to the median and remains in the range of 21 +/- 2 cm(-3). This criterion excludes the specific new particle formation events characterized with high concentration of intermediate ions and includes only most typical quiet periods between the events when the simultaneous growth, depletion and recharging of particles are described with steady-state equations. We estimated the growth rate of nanoparticles to be about 2 nm h(-1) while the growth flux or apparent nucleation rate proved to be about 0.5 cm(-3) s(-1) at 3 nm and about 0.08 cm(-3) s(-1) at 7 nm. The results suggest that the process of new particle formation is not interrupted during the quiet periods between events of intensive nucleation of atmospheric aerosols.