The number n is called an apocalyptic power if 2ⁿ contains the consecutive digits 666 (in decimal).

• ...,
• 6460,
• 6461,
• 6462,
• 6463,
• 6464,
• 6466,
• 6467,
• ...

A positive integer greater than 1 that is not prime is called composite.

Composite numbers are opposite to prime numbers.

• ...,
• 6460,
• 6461,
• 6462,
• 6463,
• 6464,
• 6465,
• 6466,
• ...

The number n is deficient if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

• ...,
• 6458,
• 6459,
• 6461,
• 6463,
• 6465,
• 6466,
• 6467,
• ...

One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.

• ...,
• 6436,
• 6440,
• 6453,
• 6463,
• 6490,
• 6503,
• 6505,
• ...

To build the lucky number sequence, start with natural numbers. Delete every second number, leaving 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, ... . The second number remaining is 3, so delete every third number, leaving 1, 3, 7, 9, 13, 15, 19, 21, ... . The next number remaining is 7, so delete every 7th number, leaving 1, 3, 7, 9, 13, 15, 21, ... . The next number remaining is 9, so delete every ninth number, etc.

Those numbers were lucky they weren't crossed out.

• ...,
• 6433,
• 6435,
• 6447,
• 6463,
• 6471,
• 6475,
• 6477,
• ...

A number is odd if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

• ...,
• 6457,
• 6459,
• 6461,
• 6463,
• 6465,
• 6467,
• 6469,
• ...

The number n is odious if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

• ...,
• 6457,
• 6458,
• 6460,
• 6463,
• 6465,
• 6466,
• 6468,
• ...

A number is said to be square-free if its prime decomposition contains no repeated factors.

• ...,
• 6458,
• 6459,
• 6461,
• 6463,
• 6465,
• 6466,
• 6467,
• ...