Next Number in Sequence
One sequence per line, terms split by comma or space (negatives, decimals and large integers are supported) - the next terms are inferred automatically.
Calculation Result
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| No. | Known terms | Model used | Basis | Formula / recurrence | Next term (predicted) |
|---|
Introduction to the tool and how to use it
Enter the first few terms of one sequence per line (comma or space separated; negative numbers, decimals, and big integers are recognized); the tool infers the next term automatically and can predict several terms ahead in one pass.
Candidates are tried in priority order: arithmetic / geometric → finite-difference polynomial (degree ≤ 6, extrapolated by the difference engine) → second-order linear recurrence an = p·an-1 + q·an-2 (solve a 2×2 system first, then least squares) → common sequences (Fibonacci, Lucas, primes, squares, cubes, triangular numbers, factorials, powers of 2, Catalan numbers) → odd/even position grouping. Every model is back-tested against the known terms and adopted only if all match; the first model that passes wins. With show other candidates enabled, any other passing model appears on its own line and is labeled candidate model.
Parameters: number of terms to predict (1~50), max terms per line for fitting (default 100, cap 500), strict mode (all known terms must match / allow tolerance given by decimal places), decimal places (output precision, also sets loose-mode tolerance), output separator.
If no model matches, the tool gives a reference next term by extending the first-order difference and marks it clearly as uncertain — it merely continues the last difference and does not guarantee a real pattern.
Limits: up to 300 lines, 500 terms per line, 50 predicted terms per run; excess is silently clamped. When an integer sequence predicts an integer, it displays as an integer (no 13.000000), and integer literals always run as exact big integers. If you only need to identify the pattern itself, use the sequence-pattern recognition tool.
Candidates are tried in priority order: arithmetic / geometric → finite-difference polynomial (degree ≤ 6, extrapolated by the difference engine) → second-order linear recurrence an = p·an-1 + q·an-2 (solve a 2×2 system first, then least squares) → common sequences (Fibonacci, Lucas, primes, squares, cubes, triangular numbers, factorials, powers of 2, Catalan numbers) → odd/even position grouping. Every model is back-tested against the known terms and adopted only if all match; the first model that passes wins. With show other candidates enabled, any other passing model appears on its own line and is labeled candidate model.
Parameters: number of terms to predict (1~50), max terms per line for fitting (default 100, cap 500), strict mode (all known terms must match / allow tolerance given by decimal places), decimal places (output precision, also sets loose-mode tolerance), output separator.
If no model matches, the tool gives a reference next term by extending the first-order difference and marks it clearly as uncertain — it merely continues the last difference and does not guarantee a real pattern.
Limits: up to 300 lines, 500 terms per line, 50 predicted terms per run; excess is silently clamped. When an integer sequence predicts an integer, it displays as an integer (no 13.000000), and integer literals always run as exact big integers. If you only need to identify the pattern itself, use the sequence-pattern recognition tool.
How to use
- Paste the first terms of each sequence into the input box, one sequence per line.
- Set the prediction count, strict mode, and tolerance decimal places; choose whether to show other candidates as needed.
- Click Run.
- Copy the predicted results.
Message board
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