MathDB

The sequence of digits

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 \dots

is obtained by writing the positive integers in order. If the

10^n

-th digit in this sequence occurs in the part of the sequence in which the

m

-digit numbers are placed, define

f(n)

to be

m

. For example,

f(2)=2

because the 100th digit enters the sequence in the placement of the two-digit integer 55. Find, with proof,

f(1987)

Problem Statement