MathDB

5.

Let x be a real number with

0<x<1

and let

0.c_1c_2c_3...

be the decimal expansion of x.Denote by

B(x)

the set of all subsequences of

c_1c_2c_3

that consist of 6 consecutive digits. For instance ,

B(\frac{1}{22})={045454,454545,545454}

Find the minimum number of elements of

B(x)

x

varies among all irrational numbers with

0<x<1

Problem Statement