Generate Rudin-Shapiro Sequence
Create Golay-Rudin-Shapiro values. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate Rudin-Shapiro Sequence
- 1. Set how many terms. Enter How many terms to decide how far into the Rudin-Shapiro sequence to compute, where each term depends on the count of consecutive 11 pairs in the index's binary form.
- 2. Set a separator. Choose Separator, a comma or newline, to shape the output for a plain list or spreadsheet column of 1s and -1s.
- 3. Copy the sequence. The tool counts occurrences of consecutive 1 bits in each index's binary representation and assigns plus one or minus one based on the parity. Copy the resulting sequence for your study.
When to use Generate Rudin-Shapiro Sequence
Generate Rudin-Shapiro Sequence produces the plus-one and minus-one sequence built from counting consecutive 1 bits in binary, known for keeping partial sums bounded in a way that has applications in signal processing and polynomial construction. Reach for it whenever you need verified terms without computing bit patterns by hand.
- Studying bounded partial sums. A student learning why the Rudin-Shapiro sequence's partial sums stay bounded, unlike a typical random plus-minus sequence, generates terms to compute and track the running sum directly.
- Building low autocorrelation signal examples. Someone studying signal processing applications where this sequence produces polynomials with small maximum values on the unit circle wants verified terms to construct an example polynomial.
- Testing a bit-pattern counting function. A developer who wrote a function to count consecutive 1 bits in a binary representation validates the derived plus-minus sequence against this tool's output.
- Cross-referencing OEIS A020985. Someone checking their manual derivation against the published sequence regenerates the early terms here to confirm an exact match with the reference source.
Examples
The first thirteen terms
Output
1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1
About the Generate Rudin-Shapiro Sequence tool
Generate Rudin-Shapiro Sequence runs as plain JavaScript in your browser tab, with no server behind it. Create Golay-Rudin-Shapiro values. Whatever you put in stays on your device from start to finish.
The tool is part of EditSafely's Math Tools section, 234 single-purpose utilities built around the same idea: open the page, get the result, keep your data to yourself.
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.
That local-first design has practical benefits beyond privacy. The tool keeps working on a flaky connection once the page has loaded, results are instant because nothing round-trips to a server, and it is safe to use with confidential material.
Frequently asked questions
Does Generate Rudin-Shapiro 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.