How many 6-digit positive integers consist only of the digits 1 and 2, and contain at least two consecutive 1s? - AMAZONAWS

How many 6-digit positive integers consist only of the digits 1 and 2, and contain at least two consecutive 1s?
Curious readers often ask: how many 6-digit positive integers made up only of digits 1 and 2 contain at least two consecutive 1s? This inquiry reflects growing interest in patterns embedded in combinatorial data, particularly as more people explore structured number sets for both practical and recreational purposes. Understanding how many such 6-digit numbers exist isn’t just an academic exercise—it reveals insight into binary-digit combinations and their unique properties.