Generate Ulam Number Sequence
Create a list of Ulam numbers. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate Ulam Number Sequence
- 1. Set how many terms. Choose how many Ulam numbers to generate, starting from 1 and 2. Each following term is the smallest number expressible as the sum of two earlier terms in exactly one way.
- 2. Pick a separator. Choose commas, spaces, or newlines for how the terms are joined, depending on whether you plan to paste the sequence into prose or a code array.
- 3. Generate and copy the sequence. The list appears the moment you generate it. Copy it into a notebook, a puzzle answer key, or a script that needs verified reference values.
When to use Generate Ulam Number Sequence
Generate Ulam Number Sequence produces the sequence where each new term is the smallest integer that is the sum of two earlier distinct terms in exactly one way. It is a slow, computationally fiddly sequence to derive by hand, so having it generated on demand saves rework.
- Verifying a brute-force implementation. You wrote code that checks every pair sum to find the next Ulam number and want a trusted reference list of the first thirty terms to confirm your uniqueness check is correct.
- Exploring an unsolved sparsity conjecture. Ulam numbers have no known closed form and their density is still debated among number theorists, so generating a long list is a practical way to look for patterns or gaps yourself.
- Answering a recreational math puzzle. A puzzle or trivia question asks for the eleventh Ulam number, and rather than tracing the unique-sum rule by hand across ten prior terms, you generate the sequence directly.
- Cross-checking against OEIS A002858. You are comparing your own derivation against the OEIS entry for Ulam numbers and want an independently generated list to spot where your manual calculation went wrong.
Examples
The first eleven Ulam numbers
Output
1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26
About the Generate Ulam Number Sequence tool
Generate Ulam Number Sequence does its work locally, right in the browser. Create a list of Ulam numbers. There is no upload step, no queue and no account, and your data never travels over the network.
It belongs to the Math Tools collection on EditSafely, a set of 234 small, focused Math utilities that share the same instant, private workspace.
You can shape the output with 2 settings, including How many terms and Separator, and the result refreshes the moment you change one. A worked example further down the page shows exactly what the tool produces for a real input.
Running locally also makes the tool fast and dependable: results appear as you type or drop a file, there is no server outage that can take it down mid-task, and confidential data can be processed without a second thought.
Frequently asked questions
Does Generate Ulam Number Sequence cost anything?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
No data leaves your device. The whole tool is JavaScript that runs inside your browser tab, so there is no upload, no server-side processing and no log of what you did. If you disconnect from the internet after the page loads, it keeps working.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
Nothing to install and no account needed. Open the page in any up-to-date browser, including on a phone or tablet, and the tool is ready.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.