Ceiling orbits of rational bases are not P-recursive
A Lean 4 / Mathlib development of the companion paper of the same name (doi:10.13140/RG.2.2.10727.82081). Fix coprime integers p > q ≥ 2 and an integer x₀ ≥ 1 and iterate the ceiling map of the rational base p/q, xₙ = ⌈p·xₙ₋₁/q⌉, with associated word wₙ = q·xₙ₊₁ − p·xₙ ∈ {0,…,q−1}, the correction that makes p·xₙ divisible by q. Four statements are compared. (A) The word of every such orbit is not P-recursive: it satisfies no nontrivial linear recurrence with polynomial coefficients. (B) At p/q = 3/2 the orbit itself is not P-recursive either; for x₀ = 1 it is the sequence A061419, which is…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-09-07-000006
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-07-000006/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-07-000006/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'