PowerDigits | Topcoder Archive

Problem Statement

Given a positive integer a, consider the infinite sequence of integers {a^0, a^1, a^2, ...}. What proportion of them begin with the digits digits?

Definition

Class:: PowerDigits
Method:: proportion
Parameters:: int, int
Returns:: double
Method signature:: double proportion(int a, int digits)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

a will be between 2 and 1000, inclusive.
digits will be between 1 and 999, inclusive.

Examples

```
2
```
```
1
```
```
Returns: 0.30102999566398114
```
The first few powers of 2 that begin with "1" are 1, 16, 128, 1024.
```
2
```
```
163
```
```
Returns: 0.0026562436437400742
```
Around 1 in 400 powers of 2 begin with "163". The first one is 16384.
```
345
```
```
678
```
```
Returns: 6.400804134383014E-4
```
```
10
```
```
42
```
```
Returns: 0.0
```
```
3
```
```
7
```
```
Returns: 0.057991946977686705
```

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.