Yes, 6 is considered an evil number according to one definition. The term "evil number" has two potential meanings based on the provided reference:
- A number whose digits sum to 666
- A nonnegative integer that has an even number of 1s in its binary expansion (Pegg and Lomont 2004).
We will explore whether 6 qualifies as an evil number under the second definition.
Evil Number Defined by Binary Representation
According to the definition where an "evil" number is a nonnegative integer with an even number of 1s in its binary expansion, we need to examine the binary representation of 6.
- Convert 6 to binary: 6 in decimal is 110 in binary.
- Count the 1s: The binary representation 110 has two 1s.
- Determine if the count is even: Since 2 is an even number, 6 fits this definition of an evil number.
Therefore, according to Pegg and Lomont (2004), 6 is an evil number because it is a nonnegative integer that has an even number of 1s in its binary expansion.
Here are the first few evil numbers to illustrate:
| Decimal | Binary | Number of 1s | Evil Number? |
|---|---|---|---|
| 0 | 0 | 0 | Yes |
| 3 | 11 | 2 | Yes |
| 5 | 101 | 2 | Yes |
| 6 | 110 | 2 | Yes |
| 9 | 1001 | 2 | Yes |
| 10 | 1010 | 2 | Yes |
| 12 | 1100 | 2 | Yes |
| 15 | 1111 | 4 | Yes |
| 17 | 10001 | 2 | Yes |
| 18 | 10010 | 2 | Yes |
| 20 | 10100 | 2 | Yes |
