# Symmetric integer generator

## World's simplest integer tool

This online utility generates a sequence of symmetric integers and prints them in the output. It can find all palindromic integers in the given range or calculate a certain number of them starting from a specific value. You can also customize the palindrome sequence by adjusting the integer separator and decorator symbols that wrap the integers. Created by math nerds from team Browserling.

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Symmetric integer generator tool
What is a symmetric integer generator?

With this browser-based program, you can print a list of integer palindromes, also known as symmetric integers. An integer is symmetric if its digits are mirrored on the right and left sides relative to the middle point. A palindromic integer can be read both from the beginning and from the end and you will get the same value. There are infinitely many palindrome integers, starting from single-digit integers, for example, "0" and "6", two-digit integers, for example, "22" and "99", three-digit "121" and "555", ten-digit "1234554321", and more. This application has two modes of operation. The first mode computes all symmetric integers in any interval. The second mode computes the specified number of consecutive symmetric integers starting from a specific integer. You can switch between these two generator modes in the options and use the start-range, end-range, start-position, and count fields below the mode switches to set the needed parameters. You can create custom integer palindrome sequences by wrapping all values in brackets, quotes, or other characters. For example, you can create a JavaScript array of integer palindromes by setting the sequence start and end characters to "[" and "]", which will produce "[2992, 3003, 3113]" or a Perl list "(767, 777, 787)". You can also wrap individual elements in quotation marks and create a list of strings '444', '454', '464' and change the separator symbol that goes between all elements. Integerabulous!

Symmetric integer generator examples
Click to use

A Range of Palindromes

In this example, we extract all symmetric integers from the range 0 to 1000 and print them separated by spaces. It turns out that there are 109 palindromes among the first one thousand integers. The integers from 0 to 9 are palindromic as they consist of a single digit. Values from 11 to 99 have mirror symmetry as both digits are duplicates. And integers from 101 to 999 have central symmetry as the digit in the center is not duplicated but the other two digits around it are duplicated.

0 1 2 3 4 5 6 7 8 9 11 22 33 44 55 66 77 88 99 101 111 121 131 141 151 161 171 181 191 202 212 222 232 242 252 262 272 282 292 303 313 323 333 343 353 363 373 383 393 404 414 424 434 444 454 464 474 484 494 505 515 525 535 545 555 565 575 585 595 606 616 626 636 646 656 666 676 686 696 707 717 727 737 747 757 767 777 787 797 808 818 828 838 848 858 868 878 888 898 909 919 929 939 949 959 969 979 989 999

**Required options**

Range start.

Range end.

Left symbol.

Right symbol.

Left symbol.

Right symbol.

Integer delimiter.

Custom Formatting

This example generates thirty comma-separated palindromes starting from the ten-thousandth position. It uses custom formatting and wraps each symmetric integer in guillemets marks and the entire sequence in curly brackets. Each palindrome consists of an odd number of digits, therefore the central digit is unique but the two side digits are reflected.

{«10001», «10101», «10201», «10301», «10401», «10501», «10601», «10701», «10801», «10901», «11011», «11111», «11211», «11311», «11411», «11511», «11611», «11711», «11811», «11911», «12021», «12121», «12221», «12321», «12421», «12521», «12621», «12721», «12821», «12921», «13031»}

**Required options**

Start position.

Count.

Left symbol.

Right symbol.

Left symbol.

Right symbol.

Integer delimiter.

Ten-digit Symmetric Values

In this example, we specify a large starting value equal to five billion and calculate ten symmetric values that follow it. We place each palindrome on a new line by using the "\n" character in the palindrome separator option. We also add the right-arrow and left-arrow glyphs before and after each value, hinting that the palindromes can be read from any direction.

🡒 5000000005 🡐
🡒 5000110005 🡐
🡒 5000220005 🡐
🡒 5000330005 🡐
🡒 5000440005 🡐
🡒 5000550005 🡐
🡒 5000660005 🡐
🡒 5000770005 🡐
🡒 5000880005 🡐
🡒 5000990005 🡐
🡒 5001001005 🡐

**Required options**

Start position.

Count.

Left symbol.

Right symbol.

Left symbol.

Right symbol.

Integer delimiter.

Pro tips
Master online integer tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlineintegertools.com/generate-symmetric-integers?&generate-range=true&range-start=0&range-end=1000&separator=%20&before-integer=&after-integer=&before-sequence=&after-sequence=

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