Integer palindromizerWorld's simplest integer tool
This online program creates a palindromic integer from the given integer by symmetrizing its digits and prints the symmetric value in the output. You can switch between three palindrome types in the options and create a mirrored palindrome, a centered palindrome, or a minimal palindrome. Created by math nerds from team Browserling.
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What is a integer palindromizer?learn more about this tool
With this browser-based utility, you can convert one or more integers into palindromes. The process of creating an integer palindrome involves adding the right digits at the end of the integer so that it forms mirror-symmetry around its middle point. There are three ways to add digits to an integer to make it palindromic. The first creates a mirror palindrome or so-called copy-reverse palindrome. This algorithm creates a copy of all integer digits, reverses them, and appends them at the end of the original integer. In this case, the size of the integer doubles as each digit on the left side will have a copy on the right side. For example, a copy-reverse palindrome of the integer 258 is 258852. The second type of palindrome is centered (also called anchored). It anchors the last digit of the integer, creates a copy of all the digits before it (that is, it copies all the digits except the last one), reverses them, and appends them at the end of the original value. In this case, all digits on the left side (except the last one) will be duplicated on the right side. An example of anchor symmetry is the value 25852 that is created from the integer 258. The last type of palindrome is minimalistic. It parses the input integer and tries to find the missing symmetry in it by copying digits from the start of the integer and appending them at the end of the integer until possible symmetry forms. For example, given the integer 1232, it's enough to copy the first digit 1 to the end of it and a symmetric value is formed 12321. Integerabulous!
Integer palindromizer examplesClick to use
This example converts five integers to fully-mirrored palindromes. It duplicates all digits and appends them at the end of the integer in reverse order. Mirrored palindromes always consist of an even number of digits because they double the length of each input integer.
1 46 1000 -3777 +56890
11 4664 10000001 -37777773 +5689009865
Example: 1232 → 12322321.
This example activates the centered palindrome mode and creates four palindromic integers. This mode slices the integer up to the last digit, creates a reverse copy of the slice, and appends it after the last digit of the integer. This way the central digit is anchored and the length of the palindrome is always an odd value because digits to the left and right always form symmetric pairs and only the central digit doesn't have a pair.
2 34 50005 1,000,000,001
2 343 500050005 1000000001000000001
Example: 1232 → 1232321.
Create Minimal Palindrome
In this example, we use the "Minimal Palidrome" option to create the shortest possible symmetric integers. In this case, the digits in the input integer are analyzed to find the shortest digital substring at the beginning of the integer that when copied to the end, creates a palindrome. For single-digit integers, this substring is empty as an integer with one digit is already palindromic (see the first integer in the input). For multi-digit integers, the substring has one or more digits but at maximum one less than the length of the integer. In the worst case, the minimal palindrome is equal to the centered palindrome.
3 466 1282 65898 100000000000
3 4664 12821 6589856 1000000000001
Example: 1232 → 12321.
Pro tips Master online integer tools
You can pass input to this tool via ?input query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
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