Odious Number Calculator

Enter a number to determine if it's an odious number, or provide a range to generate all odious numbers within it.

Odious Number Check or Generate

What Is an Odious Number?

An Odious Number is an integer whose binary representation contains an odd number of 1s. For example, the binary representation of 4 is \( 100 \), which has one \( 1 \), making it an odious number. Conversely, if the binary representation of a number contains an even number of \( 1s \), it is known as an Evil Number.

How to Determine if a Number Is Evil

  1. Convert the number to its binary form.
  2. Count the \( 1s \) in the binary representation.
  3. If the number of \( 1s \) is even, the number is evil.

Examples

Example 1: Is 100 an Odious Number?

Solution:

1. Binary Representation:

100 in binary is 1100100.

2. Count of \( 1s \):

There are 3 \( 1s \).

3. Result:

Since 3 is odd, \( 100 \) is an odious number.

Example 2: Is 444 an Odious Number?

Solution:

1. Binary Representation:

444 in binary is 110111100.

2. Count of \( 1s \):

There are 6 \( 1s \).

3. Result:

Since 6 is even, \( 444 \) is not an odious number.

Example 3: Is 2025 an Odious Number?

Solution:

1. Binary Representation:

2025 in binary is 11111101001.

2. Count of \( 1s \):

There are 8 \( 1s \).

3. Result:

Since 8 is even, \( 2025 \) is not an odious number.

First 100 Odious Numbers

  • 1
  • 2
  • 4
  • 7
  • 8
  • 11
  • 13
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  • 19
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  • 67
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  • 100
  • 103
  • 104
  • 107
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  • 115
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