E421: “Is there a density-one sequence with distinct consecutive products?”

Open

Statement	User	Model	Harness	Time
2)V2Any positive sequence with pairwise distinct nonempty consecutive-block products starts with a term at least…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Does there exist a strictly increasing density-one sequence of positive integers for which products over all…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Any positive sequence with pairwise distinct nonempty consecutive-block products starts with a term at least two.

kernel-checked, filed Tue Aug 25 2026 05:54:52 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every natural sequence satisfying the exact block-product injectivity predicate.

open, filed Tue Aug 25 2026 05:54:40 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Natural density is inlined as #(S∩[0,b))/b→1, simplifying source HasDensity over naturals. Product intervals are inclusive and require u≤v.

Scope. One infinite natural sequence and every pair of nonempty finite consecutive index intervals.