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bibkey: oeis2025a378252 authors: OEIS Foundation Inc. year: 2025 title: OEIS A378252 doi: null url: https://oeis.org/A378252 claim: A comment on OEIS A378252 conjectures that the running-sum residue sequence built from a coprime pair reaches zero exactly when the modulus is a power of two. strata_touched:

  • D5/S1/Recurrence/Parity/RatajczakDoublingZero license: citation-only triage: anchor

OEIS A378252

The main sequence of A378252 records least prime powers past a bound and is not the subject here. The relevant material is a separate comment added by Lechoslaw Ratajczak on October 13, 2025, which introduces an auxiliary sequence and states a conjecture about it.

The comment

For integers with the start value at least the modulus and the two coprime, the comment sets the first term to the start value reduced modulo the modulus, and every later term to the start value plus all earlier terms, again reduced modulo the modulus. It then conjectures that some term is zero precisely when the modulus is a power of two, with the exponent allowed to be zero.

The caller checked the page on September 9, 2026 and found the statement still presented as a conjecture.

What the Lean module states

D5/S1/Recurrence/Parity/RatajczakDoublingZero takes the recurrence as a hypothesis on an arbitrary sequence rather than constructing one, so the theorem applies to any sequence satisfying it. Two differences from the comment are deliberate and are not weakenings:

  • The requirement that the start value be at least the modulus is dropped. Neither direction uses it.
  • Indexing is from zero, so the comment’s first term is the module’s term at index one.

ASSUMED-UNVERIFIED: the identification of the comment’s b(i,j,t) with the module’s hypothesis is a human reading of the printed text, not a machine proof that the two denote the same sequence.

Search log

  • Caller reading, 2026-09-09: the seat reported checking the published and internal pages and the revision history, locating the comment at revision 16 of 2025-10-13, with revision 17 recording only a status change and no later revision adding a proof. It also reported phrase searches on the A-number, the author name, the b(i,j,t) notation, and doubling or modular-recurrence rewordings against arXiv, MathOverflow and Mathematics Stack Exchange. All returned the OEIS comment itself.
  • The seat stated it has no access to MathSciNet or zbMATH, so its receipt is 所查来源未找到 and not a claim that no proof exists anywhere.
  • Caller verification, 2026-09-09: the orchestrator computed the sequence directly and checked three separate assertions rather than accepting the seat’s reduction. See the problem entry for the readings.

Verified locator

  • URL: https://oeis.org/A378252