Open. The site labels the problem OPEN (page last edited 23 March 2026) and credits Bolan and Tang [Ta26], independently, with the sequence omitting infinitely many integers, and Tang with the bounds $n+\Omega(\log\log n)\le a_n\ll n^{688/413+o(1)}$; the omission result and Tang's bounds with upper exponent $4175/2506$ (the exponent $688/413$ is Sothanaphan's observation recorded in the paper, not one of its theorems) are pending partial claims on Tang's page and Bolan's page. The standing in the frontmatter derives from the claim pages.