Crate bs_crate

Palindrome number methods

An introduction to palindrome number

A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word (such as rotor or racecar) whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers (in decimal) are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, … (sequence A070199 in the OEIS).

Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain property and are palindromic. For instance:

• The palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, …
• The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, … (sequence A070199 in the OEIS).

It is obvious that in any base there are infinitely many palindromic numbers, since in any base the infinite sequence of numbers written (in that base) as 101, 1001, 10001, 100001, etc. consists solely of palindromic numbers.

Decimal palindromic numbers

All numbers in base 10 (and indeed in any base) with one digit are palindromic, so there are

• ten decimal palindromic numbers with one digit: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
• There are 9 palindromic numbers with two digits: {11, 22, 33, 44, 55, 66, 77, 88, 99}.
• There are 90 palindromic numbers with three digits: {101, 111, 121, 131, 141, 151, 161, 171, 181, 191, …, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999} … and so on.

Detailed properties of the palindrome numbers can be found on A070199 in the OEIS.

Crate Features

Default behaviour

The crate allows the user to:

• check if a number is a palindrome
• generate the first N palindromes

Limits and Assumptions

• Assuming that you don’t need to deal with numbers greater than 1,000,000.
• Code may panic if it is called with any values that would result in a number greater than 1,000,000 being generated.

Functions

first_n_palindromes

Generate the first N palindromes

is_palindrome

Check if a number is a palindrome