Arrays, numeration systems and Frankenstein games

AbstractWe define an infinite array A of nonnegative integers based on a linear recurrence, whose second row provides basis elements of an exotic ternary numeration system. Using the numeration system we explore many properties of A. Further, we propose and analyze a family Frankenstein of 2-player pebbling games played on a semi-infinite strip, and present a winning strategy based on certain subarrays of A. Though the strategy looks easy, it is actually computationally hard. The numeration system is then used to decide whether the family has an efficient strategy or not