Early Soviet jet aircraft seemed to follow a similar numbering trend where aircraft would appear with a (blank)-15 (i.e. MiG-15, Yak-15, La-15) and would be followed up by a 17 designated aircraft (i.e. MiG-17, Yak-17). Why do these aircraft share the number 15 and why is 17 the succeeding designation? What's their significance?
Starting in the late 1930s, Soviet aircraft service designations followed a pattern roughly similar to that of the US Navy's system that was in use until 1962. This system consisted of a designation for the manufacturer - MiG for Mikoyan-Gurevich, for example - and a number for the model of aircraft. The number was generally incremented based on how many designs that particular manufacturer had produced up to that point, and was even or odd depending on whether or not a design was a fighter (odd for fighter, even for non-fighters).
Taking MiG for a good example, we have:
>MiG-1 - failed high-altitude fighter from early WW2
>MiG-3 - improved version of the MiG-1 that saw larger production
>MiG-5 - Developed under the name DIS with the MiG-5 designation reserved for service. Experimental heavy escort fighter cancelled by the outbreak of war
>MiG-7 - Experimental development of the MiG-3 with an AM-37 engine
>MiG-9 - Early jet fighter
>MiG-11 - another attempt to re-engine the MiG-3 with an AM-37, ended up mounting an AM-38 and AM-39 instead during tests
>MiG-13 - better known as the I-250, an unusual motorjet-powered fighter that remained a prototype
>MiG-15 - the first-generation jet fighter made famous in Korea
>MiG-17 - Improved version of the MiG-15