bibkey: wu2025a389000 authors: Chai Wah Wu year: 2025 title: OEIS A389000, least k with n dividing the digit sums of k and k^2 doi: null url: https://oeis.org/A389000 claim: “Conjecture: a(9m+5) = 210^(2*m+1)-1 for m >= 0.” strata_touched:

• D5/S1/Digit/Admissibility/DigitSumSquareLeastWitness license: citation-only triage: anchor

OEIS A389000

The sequence definition is quoted from the orchestrator’s reading of the entry on 2026-09-08: the least positive integer k such that n divides both the base-ten digit sum of k and the digit sum of k^2. The entry was created on September 22, 2025; Chai Wah Wu stated the conjecture on October 1, 2025. The source rendering 210^(2*m+1)-1 means 2*10^(2*m+1)-1. The Lean module proves the two exact digit sums and minimality for every natural m.

Verified locator

• URL: https://oeis.org/A389000

The locator and attribution were supplied by the orchestrator. This sandbox performed no network verification; the orchestrator reports that revisions #56 through #70 state the conjecture without a proof.