The FDNY's numbering system can seem confusing.
The New York City Fire Department currently runs with 198 Engine Companies, 143 Truck Companies, 5 Rescue Companies, and 7 Squad Companies spread out in 214 Firehouses located across the city.
For Engines, numbers starting from 1 to 97 are on Manhattan and in the Bronx. Engines numbering from 98 to 150 were never organized. From there, Engine's 151 to 168 are on Staten Island, and from there Engine's 201 to 333 are Brooklyn and Queens. Engines numbering 169 to 200 were also never organized. The reason for missing numbers within the Boros is due to companies disbanding over the years. For example, Engine 2 used to be located in Midtown Manhattan. It is now disbanded and Rescue 1 is now located at Engine 2's former quarters.
For Ladders, 1 to 61 are on Manhattan and in the Bronx. Ladder 57 and Ladder 60 were never organized. Ladder's 62 to 75 were never organized. Ladder's 76 to 87 are on Staten Island. Ladder's 88 to 100 were also never organized. From there, Ladder's 101 to 176 are in Brooklyn and Queens. There was a Ladder 193 at one time stationed in Brooklyn from 1966 to 1968 at the quarters of Ladder 103. Again, like with the Engines, any missing numbers within those Boros are due to companies disbanding.
For Rescues, Rescue 1 is Manhattan below 125th Street, Rescue 2 has Brooklyn, Rescue 3 the Bronx and Manhattan above 125th Street, Rescue 4 has Queens, and Rescue 5 has Staten Island. Rescue 6 was placed into service for a short time, I believe, at Ladder 20's quarters in Lower Manhattan, but is only used now during special events. Rescue 7 is a Reserve Rescue and is not an active company. For Squads, Squad 1 is the Western half of Brooklyn and Staten Island, Squad 18 is Lower Manhattan, Squad 41 is the Western Bronx and Upper Manhattan, Squad 61 is the Eastern Bronx, Squad 252 is Eastern Brooklyn, and Squad's 270 and 288 are in Queens. For Marine Units, Marine 1 is located on Manhattan along the Hudson River, Marine 6 in Brooklyn along the East River, and Marine 9 on Staten Island in the Harbor.
Some companies and their designations were disbanded, then brought back.
Also, at one time, Brooklyn was it's own city with it's own fire department. Thus, the old BFD number designations were changed to the 200 and 100 series after the FDNY expanded into Brooklyn following Brooklyn's merger with Manhattan in the late 1890's.
I believe part of the reason why some company numbers were never organized was because the department anticipated the creation of new companies during it's phases of growth and expansion, thus some number designations may have been held in reserves for just that purpose.