bibkey: ratajczak2024a375007 authors: Lechoslaw Ratajczak year: 2024 title: A375007 — isolated quotient-remainder values doi: null url: https://oeis.org/A375007 claim: The entry conjectures that every term after the sixth has prime successor; it reports verification below 10^8. strata_touched:

• D5/S3/Arith/IsolatedQuotientRemainder license: citation-only triage: anchor

A375007

Verified locator

Canonical entry URL: https://oeis.org/A375007

The source is revision 9 (2024-08-18). OEIS entries have no DOI; the canonical URL identifies this entry.

The sequence consists of positive integers t for which t mod k = floor((t-k)/k) mod k, with 1<=k<=t, holds only at k=1 and k=t. Revision 9 (2024-08-18) conjectures that a(n)+1 is prime for n>6 and reports verification for terms below 10^8. The first six terms are 1,2,3,4,8,24. No proof of this conjecture appears in the complete entry. Its separate Fortunate-type conjecture is not addressed.

Proof scope

Mathlib’s Nat.minFac_prime, Nat.minFac_dvd and Nat.minFac_le_div supply the standard ordered factorization of a composite number. The Lean proof uses two explicit factor constructions and is a repository derivation, not a proof attributed to this OEIS entry. No publication priority or exhaustive literature coverage is claimed.