MathDB

In the sequence of powers of

2

(written in the decimal system, beginning with

2^1 = 2

) there are three terms of one digit, another three of two digits, another three of

3

, four out of

4

, three out of

5

, etc. Clearly reason the answers to the following questions: a) Can there be only two terms with a certain number of digits? b) Can there be five consecutive terms with the same number of digits? c) Can there be four terms of n digits, followed by four with

n + 1

digits? d) What is the maximum number of consecutive powers of

2

that can be found without there being four among them with the same number of digits?

Problem Statement