Detect the pattern, see the real formula, predict exactly β with honest confidence
Type a sequence β detection runs live as you edit. Separate numbers with commas, spaces or new lines.
Wiggle room forgives rounded decimals
One tap loads it into the detector
Statistics, growth behavior and the full difference triangle β updated live.
Each level is the gaps of the level above. A truly constant level (highlighted) pins down a polynomial of that degree.
| Pair | Division | Ratio |
|---|
Extends your sequence using the detected rule. Integer patterns are computed with exact big-number arithmetic β no rounding, ever.
Build sequences from classic rules or your own formula β no coding, updates live.
The formulas behind the classics β tap βtry itβ to load one into the detector.
Catalog numbers from the On-Line Encyclopedia of Integer Sequences β the detector recognizes all of these.
| OEIS | Name | First terms |
|---|
Arithmetic: the gaps between neighbors are all equal. Two seed terms fix the rule; every further term is a real verification.
Geometric: each term divided by the previous gives the same ratio β including negative ratios for alternating signs.
Polynomial: repeatedly take differences; a genuinely constant level of degree d pins a degree-d formula. The constant level must contain at least 3 equal values, otherwise it proves nothing.
Recursive: solves aβ = pΒ·aβββ + qΒ·aβββ from your first terms, then checks the rest. Fibonacci, Lucas, Pell and Jacobsthal all live here.
Famous sequences: exact lookup against primes, factorials, Catalan and friends β even if you start mid-sequence.
The overfitting trap: any k numbers sit on some degree-(kβ1) polynomial, so a formula that merely touches every point proves nothing. This tool only reports patterns verified by terms beyond those needed to build the rule β and tells you how many.
What is a sequence? An ordered list of numbers following a rule. Each term has a position n, and the rule tells you how to get the value at any position β explicitly (a formula in n) or recursively (from earlier terms).
Where they show up: compound interest grows geometrically, evenly spaced payments are arithmetic, algorithm costs are often polynomial, and Fibonacci numbers appear in sunflower spirals and pinecones.
Reading the triangle: constant 1st differences mean linear; constant 2nd differences mean quadratic β the same trick Babbage built into his Difference Engine to compute tables with nothing but addition.