# 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=

All integer tools

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Quickly print a list of integers that are palindromes.

Quickly convert the given integer to a palindromic integer.

Quickly find all integers in the given text or string.

Quickly make integer digits go in a triangle wave.

Quickly unleash the destructive force of Zalgo on integers.

Quickly find two or more integers that add up to the given integer.

Quickly find several integers that multiply up to the given integer.

Quickly randomize the given sequence of integers.

Quickly mix the order of digits in an integer.

Quickly put integers in increasing or decreasing order.

Quickly sort the individual digits of an integer.

Quickly increase all integers by a certain amount.

Quickly increase individual digits by a certain amount.

Quickly decrease all integers by a certain amount.

Quickly decrease individual digits by a certain amount.

Quickly randomly select an integer from a list of integers.

Quickly create groups from the digits of an integer.

Quickly write integer digits backwards.

Quickly remove one or more digits from an integer.

Quickly replace one or more digits in an integer.

Quickly drop digits from an integer and make it shorter.

Quickly add the thousands separator to integers.

Quickly remove the thousands separator from integers.

Quickly find the largest integer in a list of integers.

Quickly find the smallest integer in a list of integers.

Quickly find the total sum of a bunch of integers.

Quickly find the sum of all the digits in an integer.

Quickly find the total product of a bunch of integers.

Quickly find the product of all the digits in an integer.

Quickly calculate the partial sum of a bunch of integers.

Quickly calculate the partial product of a bunch of integers.

Quickly flip the sign of one or more integers.

Quickly split an integer into chunks of a given length.

Quickly merge partial integers together to form a larger integer.

Quickly round integers up or down to the required precision.

Quickly convert integers to a downloadable picture.

Quickly generate a list of von Neumann ordinals.

Quickly generate a list of Zermelo ordinals.

Quickly generate an ordered sequence of integers.

Quickly generate an ordered list of even integers.

Quickly generate an ordered list of odd integers.

Quickly write an integer spelling in words.

Quickly convert spelled integers to regular integers with digits.

Quickly generate an array of integers for programming.

Quickly find the number of occurrences of digits in integers.

Coming soon
These integer tools are on the way

Draw von Neumann Universe

Create a drawing that visualizes von Neumann hierarchy of sets.

Create Integer n-Tuples

Generate a list of tuples of integers with n elements.

Convert Integers to Unary Base

Quickly convert integers to base one.

Convert Unary Base to Integers

Quickly convert base one to integers.

Convert Integers to Binary Base

Quickly convert integers to base two.

Convert Binary Base to Integers

Quickly convert base two to integers.

Convert Integers to Octal Base

Quickly convert integers to base eight.

Convert Octal Base to Integers

Quickly convert base eight to integers.

Convert Integers to Hex Base

Quickly convert integers to base sixteen.

Convert Hex Base to Integers

Quickly convert base sixteen to integers.

Convert Integers to Base64

Quickly encode integers to base-64.

Convert Base64 to Integers

Quickly decode base-64 to integers.

Change Integer Base

Quickly convert integers to a custom base.

Convert Integers to HTML Entities

Quickly encode integers to HTML encoding.

Convert HTML Entities to Integers

Quickly decode HTML entities to integers.

Convert Integers to URL Encoding

Quickly encode integers to URL (percent) encoding.

Convert URL Encoding to Integers

Quickly decode URL-encoded integers.

Convert Signed Integer to Unsigned

Quickly convert a signed integer to an unsigned integer.

Convert Unsigned Integer to Signed

Quickly convert an unsigned integer to a signed integer.

Create Random Integers

Generate a list of random integers.

Check if an Integer is Symmetric

Check if the given integers are palindromes.

Generate an Integer Matrix

Create a matrix whose entries are all integers.

Generate an Integer Vector

Create a vector with integer coefficients.

Find the Average

Quickly calculate the average value of integers.

Find the Digit Average

Quickly calculate the average value of integer digits.

Clamp Integers

Limit integer values to a range.

Clamp Integer Digits

Limit integer digit values to a range.

Duplicate Integers

Create multiple copies of the input integers.

Rotate Integers

Rotate the digits of an integer to the left or right.

Shift Integer Digits

Move the digits of an integer to the left or right.

Subtract Integers

Quickly find the difference of a bunch of integers.

AND Integers

Quickly apply the bitwise AND operation to integers.

OR Integers

Quickly apply the bitwise OR operation to integers.

XOR Integers

Quickly apply the bitwise XOR operation to integers.

NOT Integers

Quickly apply the bitwise NOT operation to integers.

NAND Integers

Quickly apply the bitwise NAND operation to integers.

NOR Integers

Quickly apply the bitwise NOR operation to integers.

XNOR Integers

Quickly apply the bitwise NXOR operation to integers.

Convert an Integer to Ordinal

Add -st, -nd, -rd, -th suffixes to integers to make them ordinals.

Convert an Oridinal to Integer

Remove -st, -nd, -rd, -th suffixes from ordinals to make them ints.

Filter Integers

Find integers that match a filter (greater, less, equal).

Left-pad Integers

Add padding to integers on the left side.

Right-pad Integers

Add padding to integers on the right side.

Right-align Integers

Position all integers so that they align on the right.

Center Integers

Position all integers so that they align in the middle.

Take Absolute Value of Integers

Turn all integers into positive integers.

Make All Integers Negative

Turn all integers into negative integers.

Convert Integers to Fractions

Rewrite an integer in fractional form.

Convert Fractions to Integers

Extract the numerator and denominator from a fraction.

Find and Replace Integers

Search for all occurrences of an integer and replace it.

Generate Integers from a Regex

Create integers that match the given regular expression.

Generate Small Integers

Create relatively tiny integers.

Generate Big Integers

Create relatively huge integers.

Generate Oscillating Integers

Create a sequence of oscillating integers, such as 123212321.

Color Integers

Add color to integers based on a condition.

Color Integer Digits

Add color to individual digits in the given integers.

Draw an Integer Spiral

Make the digits of an integer go in a spiral shape.

Draw an Integer Circle

Make the digits of an integer go in a circle.

Draw an Integer Box

Fill a box with certain width and height with digits.

Create 2D Integers

Use ASCII art to convert integers to 2-dimensional drawings.

Create 3D Integers

Use ASCII art to convert integers to 3-dimensional drawings.

Decompose an Integer

Decompose an integer into ones, tens, hundreds, etc.

Find Patterns in Integers

Find hidden patterns of numbers in integers.

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