bibkey: granvik2024a292273
authors: Mats Granvik
year: 2024
title: "OEIS A292273, real-part formula for the even-supported signed Mobius function"
doi: null
url: https://oeis.org/A292273
claim: "Conjecture: a(n) = Re(A008683(n)*(i^n)). - Mats Granvik, Jul 06 2024"
strata_touched:
  - D5/S3/Arith/Mobius/GranvikMobiusRealPart
license: citation-only
triage: anchor

Granvik’s A292273 real-part formula

The source definition is: “For odd n: a(n) = 0, and for even n: a(n) = -mu(n), where mu is Moebius function (A008683).” The offset is one. The conjecture is: “Conjecture: a(n) = Re(A008683(n)*(i^n)). - Mats Granvik, Jul 06 2024”. The exponent is the natural index, mu is the ordinary integer Mobius function and i is the complex imaginary unit.

The arithmetic definition and real-part identity concern every positive index. The Collatz-trajectory interpretation in the comment and program sections is outside this assertion. No trajectory-termination assumption or conclusion is used.

Verified locator

• Declared URL: https://oeis.org/A292273
• Primary internal-page locator: https://oeis.org/A292273/internal
• Revision history: https://oeis.org/history?seq=A292273
• Official source export, pinned to its latest entry-changing commit: https://github.com/oeis/oeisdata/blob/571197984aeda7b8b680fe3a1f6a43f9898cd441/seq/A292/A292273.seq
• Export header: %I A292273 #24 Jul 06 2024 14:02:30.
• %N contains the arithmetic definition above; %O is 1; %F contains the real-part conjecture and its Granvik attribution.
• The direct internal page returned HTTP 403. The official current and pinned exports were read successfully and agree on these source clauses. The pinned export SHA-256 is 324317d351e46d301208420ea049ac5e6b1404295c159f29a4ffe866a450cc29.

Scope and reuse

The generic squarefree criterion for vanishing Mobius values and periodic powers of i are supplied by Mathlib at revision 56a005855ea17e0b0958f73ec801ae140b0a1679. Their composition proves the arithmetic identity; no generic result is claimed as new.

The bounded source qualification covered the primary entry and history, related OEIS entries, arXiv, Math/MathOverflow, GitHub Lean/formal-conjectures and Sequencelib, plus the repository’s existing declarations and source material. No exact prior answer was found in those inspected scopes. Absence of a proof from all published literature remains ASSUMED-UNVERIFIED; a search miss does not establish priority.

Only the source clauses needed to identify this assertion are quoted. No license to redistribute the full OEIS entry is asserted.