I often have to generate triangle numbers so I created this simple online utility that does it for me. It lets you generate however many triangular numbers you need starting from any position or value. It works in the browser and is powered by alien technology from the future.

Triangle Number Generator Options

Starting Position or Value
Count and Separator
Base

Triangle Number Generator Examples (click to try!)

Triangular Numbers from T(100)
This example computes fifty triangle numbers starting from T100. The 100th number is calculated via the expression 100(100+1)/2 and is equal to 5050, the 101st number is calculated via 101(101+1)/2 = 5151, and so on. All computed numbers are separated by the comma symbol.
5050, 5151, 5253, 5356, 5460, 5565, 5671, 5778, 5886, 5995, 6105, 6216, 6328, 6441, 6555, 6670, 6786, 6903, 7021, 7140, 7260, 7381, 7503, 7626, 7750, 7875, 8001, 8128, 8256, 8385, 8515, 8646, 8778, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 10011, 10153, 10296, 10440, 10585, 10731, 10878, 11026, 11175
Start from a Position
Find triangular numbers starting from this position.
How many values to generate?
Separate triangular numbers with this value.
Decimal Base
The Beast Triangular Number
This example outputs a list of ten triangle numbers that are greater or equal to the beast number 666. It happens that T6×6 = 666. To print this list, it uses the "Start from a Value" generator mode and specifies 666 below it. All numbers are printed on separate lines.
666
703
741
780
820
861
903
946
990
1035
Start from a Value
Find triangular numbers bigger or equal to this value.
How many values to generate?
Separate triangular numbers with this value.
Decimal Base
Hex Triangular Numbers
In this example, we print a sequence of five triangle numbers in the hexadecimal base. We set the starting position to obscurely large position (2 billion) to show you that this tool can work with very large numbers. Note that triangle numbers grow quadratically fast (asymptotic to n2).
1bc16d678a62ca00
1bc16d6801985e01
1bc16d6878cdf203
1bc16d68f0038606
1bc16d6967391a0a
Start from a Position
Find triangular numbers starting from this position.
How many values to generate?
Separate triangular numbers with this value.
Hexadecimal Base

How Does This Triangle Number Generator Work?

This triangle number generator works entirely in your browser and is written in JavaScript. It can calculate triangular integers starting from any position or any value. It uses the mathematical formula T(n) = n(n+1)/2 to find the n-th triangle number. If the starting value is given, then it inverts the formula by first multiplying both sides by two 2T(n) = n(n+1), then expanding the n(n+1) term to 2T(n) = n2 + n, and then bringing all terms to one side n2 + n - 2T(n) = 0. The solution to this quadratic equation gives us the starting index n = (sqrt(1+8x) - 1)/2. To find count (specified in options) numbers, it uses a loop from 1 to n and at every iteration computes T(n). All T(n) values are converted to the given base (specified in options) and are saved for output in a variable tNumbers. As the triangle numbers grow quickly, this tool uses the bignumber.js library to support arbitrary large computations. When the output variable tNumbers is printed, the values are combined together and the separator symbol is placed between them. The separator symbol can be set in the options.

Created by Browserling

This triangle number generator was created by me and my team at Browserling. Behind the scenes, it's actually powered by our programmer tools that are used by millions of people every month. Browserling itself is an online cross-browser testing service powered by alien technology. Check it out!

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