Pattern discovery

The algo_discovery package ranks candidate hypotheses for an integer sequence and scores them with confidence, an explanation, and (when applicable) a predicted next term.

CLI

uv run python -m algo_discovery 1 4 9 16 25

Python API

from algo_discovery import DiscoveryEngine

engine = DiscoveryEngine()

# Squares
result = engine.discover((1, 4, 9, 16, 25))
print(result.best.name)        # "quadratic"
print(result.best.prediction)  # 36

# Subset of hypotheses only
from algo_discovery.engine import hypotheses_by_name
engine = DiscoveryEngine(hypotheses=hypotheses_by_name(["arithmetic", "fibonacci-like"]))

Built-in hypotheses

Hypothesis	Detects
constant	identical terms
arithmetic	constant differences
geometric	constant ratios
quadratic	constant second differences
cubic	constant third differences
powers-of-two	2^n growth ladder
fibonacci-like	recurrence a(n) = a(n-1) + a(n-2)
affine-recurrence	general linear recurrences
prime	primes / prime-like patterns
alternating-sign	sign oscillation

Each yields a confidence (0–1), an explanation string, and a predicted next term when it fits.

Feature extraction

Every hypothesis sees the same feature vector derived from the sequence: differences, ratios, sign patterns, monotonicity, palindromicity, growth rate, gcd, and a normalized numeric encoding.