A palindromic prime is a prime which is a palindrome.

In base 2 Mersenne primes are palindromic primes.

• ...,
• 353,
• 373,
• 383,
• 727,
• 757,
• 787,
• 797,
• ...

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.

• ...,
• 723,
• 724,
• 725,
• 727,
• 729,
• 730,
• 731,
• ...

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.

• ...,
• 699,
• 717,
• 723,
• 727,
• 729,
• 735,
• 739,
• ...

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.

• ...,
• 721,
• 723,
• 725,
• 727,
• 729,
• 731,
• 733,
• ...

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

Guess what evil numbers are.

• ...,
• 721,
• 722,
• 724,
• 727,
• 728,
• 731,
• 733,
• ...

A palindrome is a number that reads the same forward or backward.

• ...,
• 696,
• 707,
• 717,
• 727,
• 737,
• 747,
• 757,
• ...

A prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.

Prime numbers are opposite to composite numbers.

• ...,
• 701,
• 709,
• 719,
• 727,
• 733,
• 739,
• 743,
• ...

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

• ...,
• 719,
• 721,
• 723,
• 727,
• 730,
• 731,
• 733,
• ...

Undulating numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.

• ...,
• 696,
• 707,
• 717,
• 727,
• 737,
• 747,
• 757,
• ...