LODA is an assembly language, a computational model, and a distributed tool for mining programs. You can use it to generate and search programs that compute integer sequences from the On-Line Encyclopedia of Integer Sequences® (OEIS®). The goal of the project is to reverse engineer formulas and efficient algorithms for a wide range of non-trivial integer sequences.

The LODA Language

LODA means Lexicographical Order Descent Assembly. It is an assembly-based language for solving number-theoretic problems. It has a simple syntax and a rich set of arithmetic operations. This enables an automated search of new programs and algorithms using a process called program mining. In a nutshell, we use distributed compute power, smart search algorithms and machine-learning to find programs and formulas for the integer sequences from the OEIS database.

To get an idea of the language, you can search browse through the available programs or search using keywords. A comprehensive overview of the language concepts and the supported operations is available in the language specification.


Running the LODA miners is a community project. We are grateful for the many contributions we receive. Here is a list of the top contributors of the LODA BOINC project. If you have spare compute power and like to contribute to the project, please checkout our mining info page.

The source code of LODA is hosted in the loda-lang organization on GitHub. Please open issues if you find bugs or if you have feature requests. For generation questions, please use discussions. If you would like to contribute code, please contact us on GitHub or via e-mail.

  • Sequence Machine is a database of mathematical conjectures on many machine-generated integer and decimal sequences.
  • Superseeker from the OEIS is an automatic email server for identifying integer sequences.
  • jOEIS is a collection of pure Java programs implementing sequences from the OEIS.
  • NumberFields@home is a BOINC project to do research in number theory.
  • The Ramanujan Machine is an algorithmic approach to discover new mathematical conjectures.
  • QSynt is a program synthesis tool for OEIS integer sequences.
  • OEIS-Search-GCD-reduced is an extended search in OEIS with GCD reduction and data variants.