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Benchmarking Large Language Models with Integer Sequence Generation Tasks
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Introduces an OEIS-based benchmark of 1000 integer sequence generation tasks, evaluating 21 LLMs on Python code generation under time limits, with an LLM-based lookup-table cheating detector.
Problem
Existing math and code benchmarks do not rigorously test algorithmic reasoning on open-ended integer sequences, and models may memorize sequence values rather than compute them.
Approach
Uses OEIS integer sequences (with a split of pre-July-2024 "classic" and post-cutoff "contemporary" sequences, and easy/hard labels) as test cases, enforces runtime limits, and flags lookup-table cheating with an LLM judge validated against a human evaluator.
Key results
- o3 achieves 73.6% average score and 68.4% perfect on contemporary easy sequences (4s timeout), versus 39.5% for gpt-4o.
- On contemporary hard sequences, the best average is o3-mini at 32.0 and o3 has the highest perfect rate at only 4.4%, showing low performance on hard sequences.
- The GPT-4o cheating detector reached 95% agreement with a human evaluator after adding six labeled examples to the prompt (86% zero-shot).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use reasoning-focused models instead of general-purpose models | LLMs generating OEIS sequence code · Contemporary SequenceEasy and SequenceHard | average accuracy score | Helped |
| Allow a 4s code timeout instead of 0.5s | Reasoning-focused models · Contemporary SequenceHard | average accuracy score | Helped |
| Allow a 4s code timeout instead of 0.5s | LLMs on contemporary sequences · Contemporary SequenceEasy | average accuracy score | No clear effect |
| Generate code for hard sequences rather than easy sequences | Evaluated LLMs · OEIS benchmark | average accuracy score | Hurt |
| Use memoization to reuse previously verified primes | o3 on sequence A380521 · A380521 | execution within time constraints | Helped |
Surprising findings
- Models with the lowest cheating rates were not the strongest models, and cheating regressed within model series (e.g., o3 cheated more than o1 on hard sequences).
- Gemini 1.5 pro cheated on 66.7% of hard sequences despite prompting not to use lookup tables.
Limitations
- Reliance on OEIS may introduce bias in sequence types and subjective easy/hard labels; some OEIS sequences have public code snippets.
- The LLM cheating detector is not perfect (95% human agreement), and cheating judgment is partly subjective.
- Evaluation restricted to Python standard library and fixed time limits, which may penalize correct but slow solutions.
Experimental setup
Datasets: OEIS
Benchmarks: OEIS integer sequence benchmark (1000 sequences: contemporary and classic, easy and hard)
Metrics: average accuracy score percent perfect sequences percent flagged for cheating timeout-based pass rate
Baselines: gpt-4o gpt-4o-mini gpt-3.5-turbo claude-3.7-sonnet llama-405b gemini-1.5-pro
Builds on: OEIS
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