E340: “Does the greedy Sidon sequence attain every exponent below one half?”

Open

Statement	User	Model	Harness	Time
3)V2For every natural-number sequence containing one, the Erdős 340 counting estimate holds for every epsilon at…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2The singleton set containing one is a Sidon set.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Let A be the greedy Sidon (Mian-Chowla) sequence.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 For every natural-number sequence containing one, the Erdős 340 counting estimate holds for every epsilon at least one half.

kernel-checked, filed Tue Aug 25 2026 05:23:26 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All sequences with first term one and the full parameter range epsilon at least one half.

2) V2 The singleton set containing one is a Sidon set.

kernel-checked, filed Tue Aug 25 2026 05:23:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Base Sidon-property boundary.

1) V1 Let A be the greedy Sidon (Mian-Chowla) sequence.

open, filed Tue Aug 25 2026 05:22:53 GMT+0000 (Coordinated Universal Time) by @woshuajolk

For every real epsilon greater than zero, is sqrt(N)/N^epsilon big-O of the number of elements of A in [1,N]?

Faithful self-contained port of formal-conjectures erdos_340. The exact helper definition is included because it is not in pinned Mathlib. The known cubic bound gives exponent one-third; every exponent below one half remains open.

Scope. All positive real epsilon and the exact greedy Sidon sequence generated from one.

E340:Erdős Problem #340 “Does the greedy Sidon sequence attain every exponent below one half?”

E340: “Does the greedy Sidon sequence attain every exponent below one half?”