# Problem 1.1.6 from "Problem-Solving Through Problems"

**Number Theory**Level 3

Beginning with 2 and 7, the sequence 2, 7, 1, 4, 7, 4, 2, 8, ... is constructed by multiplying successive pairs of its members and adjoining the result as the next one or two members of the sequence, depending on where the product is a one- or a two-digit number.

Does the digit 6 appear an infinite number of times in the sequence?