Let $A\subset \mathbb{N}$ be an infinite Sidon set. Is it true that$$\underset{x\to \infty }{\mathrm{liminf}}\frac{|A\cap [1,x]|}{x^{1/2}}(\log x{)}^{1/2}=0?$$Does there exist an infinite Sidon set $A$ such that$$\underset{x\to \infty }{\mathrm{liminf}}\frac{|A\cap [1,x]|}{x^{1/2}}(\log x{)}^c>0$$for some $c>0$?

Vela Sidon frontier (A309370) · verified work

A B₂/Sidon problem — the same object family as Vela's verified Sidon records, where nine improved terms were accepted into OEIS A309370 (the campaign's first external adoption).

OEIS A309370 ↗ · verified-combinatorics (witnesses + verify.py) ↗ · the Erdős campaign