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

• ...,
• 1139,
• 1140,
• 1141,
• 1155,
• 1157,
• 1158,
• 1160,
• ...

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

Composite numbers are opposite to prime numbers.

• ...,
• 1150,
• 1152,
• 1154,
• 1155,
• 1156,
• 1157,
• 1158,
• ...

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.

• ...,
• 1151,
• 1153,
• 1154,
• 1155,
• 1156,
• 1157,
• 1159,
• ...

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

Guess what odious numbers are.

• ...,
• 1148,
• 1151,
• 1152,
• 1155,
• 1157,
• 1158,
• 1161,
• ...

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.

• ...,
• 1117,
• 1123,
• 1147,
• 1155,
• 1167,
• 1179,
• 1183,
• ...

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.

• ...,
• 1149,
• 1151,
• 1153,
• 1155,
• 1157,
• 1159,
• 1161,
• ...

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

• ...,
• 1151,
• 1153,
• 1154,
• 1155,
• 1157,
• 1158,
• 1159,
• ...

The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.

• ...,
• 1101,
• 1103,
• 1125,
• 1155,
• 1157,
• 1164,
• 1167,
• ...