The phrase "a steadily increasing number" is correct and usable in written English.
It can be used to describe a quantity that is consistently growing over time.
Example: "The study revealed a steadily increasing number of participants in the program over the last five years."
Alternatives: "a continually rising number" or "an ever-growing number".
This new digital world offers a steadily increasing number of choices.
A steadily increasing number of Sunni militant jihadists from outside Syria have also joined the fray since mid-July.
No surprise, then, that a steadily increasing number of foreigners are pitching up here – inquisitive individuals, rather than tour groups.
The past two decades have seen a steadily increasing number of papers on bubble columns and related reactors.
The city, meanwhile, is receiving a steadily increasing number of reports of abuse and neglect — 65,856 in 2008, up from 63,434 the year before.
"On the other hand a steadily increasing number of serious crimes, including murder and rapes, are being solved and criminals brought to justice with its help.
In the past five years, a steadily increasing number of schoolchildren — as many as 15,000 a year — have come here for a course on Confucian etiquette.
On the other, a steadily increasing number of clubs, among whom the Broncos are just the most extreme example, are broke and unviable.
After four years without international inspections a steadily increasing number of industrial, administrative, military, scientific and research sites are again being opened for inspections under the authority of the Security Council.
The federal data shows no tire-related fatalities involving Explorers from 1991 to 1993 and a steadily increasing number thereafter, which may reflect that tread separation becomes more common as tires age.
In addition to easels, paints, and brushes, and a steadily increasing number of paintings, Curtis regularly creates scores of three-dimensional shadow boxes that he calls "my little touches of memory".
