My understanding of the word consequentive is that it is used to describe events or numbers that do follow a pattern, but are not necessarily consecutive.
For example, you could refer to the Olympic Games held between 1988 and 2000 as being consecutive games, but they were held over consequentive years (1988, 1992, 1996 & 2000). They cannot be described as being held over consecutive years, as they were not.
Another example would be saying that last week we experienced five consequentive nights of minus zero temperatures; this could refer to two nights of -2, then one night of +1, followed by three nights of -2.
I believe this is the true meaning of the word but, as with so many of our words, it has become lost in translation over the years and is so rarely used nowadays that it is pretty much unheard of.
Hope that helps?