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

• ...,
• 3651,
• 3652,
• 3654,
• 3655,
• 3656,
• 3657,
• 3659,
• ...

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

Composite numbers are opposite to prime numbers.

• ...,
• 3652,
• 3653,
• 3654,
• 3655,
• 3656,
• 3657,
• 3658,
• ...

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.

• ...,
• 3651,
• 3652,
• 3653,
• 3655,
• 3656,
• 3657,
• 3658,
• ...

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.

• ...,
• 3621,
• 3625,
• 3633,
• 3655,
• 3661,
• 3663,
• 3669,
• ...

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.

• ...,
• 3649,
• 3651,
• 3653,
• 3655,
• 3657,
• 3659,
• 3661,
• ...

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

Guess what evil numbers are.

• ...,
• 3649,
• 3650,
• 3652,
• 3655,
• 3656,
• 3659,
• 3661,
• ...

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

• ...,
• 3649,
• 3651,
• 3653,
• 3655,
• 3657,
• 3658,
• 3659,
• ...

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.

Compare to square, pentagonal and tetrahedral numbers.

• ...,
• 3403,
• 3486,
• 3570,
• 3655,
• 3741,
• 3828,
• 3916,
• ...