# Learning Program Synthesis for Integer Sequences from Scratch

arXiv: https://arxiv.org/abs/2202.11908 · HTML: https://mlsanity.com/paper/2202.11908/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 4 of 4)

- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Tree Neural Networks in HOL4](https://mlsanity.com/paper/2009.01827/) (2020)

## Built on by (most cited first, 8 of 8)

- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (2024)
- [IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation](https://mlsanity.com/paper/2509.26076/) (2025)
- [Alien Coding](https://mlsanity.com/paper/2301.11479/) (2023)
- [MizAR 60 for Mizar 50](https://mlsanity.com/paper/2303.06686/) (2023)
- [Learning Conjecturing from Scratch](https://mlsanity.com/paper/2503.01389/) (2025)
- [A Llama walks into the 'Bar': Efficient Supervised Fine-Tuning for Legal Reasoning in the Multi-state Bar Exam](https://mlsanity.com/paper/2504.04945/) (2025)
- [IntSeqBERT: Learning Arithmetic Structure in OEIS via Modulo-Spectrum Embeddings](https://mlsanity.com/paper/2603.05556/) (2026)
- [Artifical intelligence and inherent mathematical difficulty](https://mlsanity.com/paper/2408.03345/) (2024)

## Abstract (arXiv)

We present a self-learning approach for synthesizing programs from integer sequences. Our method relies on a tree search guided by a learned policy. Our system is tested on the On-Line Encyclopedia of Integer Sequences. There, it discovers, on its own, solutions for 27987 sequences starting from basic operators and without human-written training examples.