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Where Induction Runs Out: Description-Length Difficulty and the Memorisation Gap in Integer-Sequence Benchmarks

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

Integer sequences from the On-Line Encyclopedia of Integer Sequences (OEIS) are increasingly used to benchmark mathematical reasoning in language models. We ask what such benchmarks actually measure, using an exactly computable reference learner: two-part minimum description length (MDL) over the class of P-recursive (holonomic) recurrences, evaluated on every prefix of a sequence as terms arrive. Three findings follow. First, MDL difficulty is a parameter count. The discovery point nd, the first prefix length at which a symbolic hypothesis beats verbatim storage, is predicted almost exactly b

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