integer-sequence-research

Discovers and validates integer sequences using adversarial cross-validation and OEIS collision checks.

1|Updated Mar 17, 2026

Search Tags:#validation #sequence #falsification #factorization #conjectures #oeis #multiplicativity

Ready to run

npx skills add https://github.com/daedalus/skills --skill integer-sequence-research

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: integer-sequence-research
Source: https://github.com/daedalus/skills/tree/main/skills/OEIS
Command: npx skills add https://github.com/daedalus/skills --skill integer-sequence-research

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy.

What problem does it solve?

Autonomous, end-to-end research for discovering, validating, and characterizing integer sequences suitable for OEIS submissions, reducing manual conjecture and verification effort.

Core Features & Use Cases

Adversarial research pipeline that generates candidate sequences, cross-validates with multiple implementations, and aggressively falsifies conjectures.
Multiplicativity detection, prime-power profiling, and Dirichlet-convolution style constructions to map sequence behavior.
OEIS collision checks to assess novelty and guide publication-worthy sequence discovery.

Quick Start

Run the autonomous sequence research pipeline by executing python seq_research.py.

Frequently Asked Questions about integer-sequence-research

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I discover novel integer sequences for OEIS submission?▼

To discover novel integer sequences for OEIS submission, you can run an autonomous adversarial pipeline that generates candidates, cross-validates them, and checks for OEIS collisions to ensure novelty. Execute the research script using Python.

How does an adversarial pipeline validate mathematical conjectures about sequences?▼

An adversarial pipeline validates mathematical conjectures by aggressively falsifying generated candidates through cross-validation across multiple implementations, ensuring only robust and provably valid sequences survive the testing phase.

Do I need SymPy to detect multiplicativity and perform factorization in sequence research?▼

Yes, you need SymPy and standard math libraries to perform sequence research. SymPy is required to execute the modular arithmetic, factorization, and multiplicativity detection needed to profile sequence behavior accurately.

What is the best way to profile prime-power behavior in integer sequences?▼

The best way to profile prime-power behavior in integer sequences is using a research pipeline that applies Dirichlet-convolution-based constructions and prime-power profiling to map sequence behavior and identify OEIS-worthy patterns.

Can I check if a generated sequence collides with existing OEIS entries?▼

Yes, you can check for OEIS collisions by running the autonomous sequence research pipeline, which specifically assesses novelty by checking generated candidates against existing OEIS entries to guide publication-worthy discovery.

What are the limitations of automated sequence generation and falsification?▼

Automated sequence generation and falsification is limited by its dependency on a working Python environment with SymPy and relies on cross-validating multiple implementations to avoid false positives in conjecture verification.