This interactive browser visualization overlays the integer sequence OEIS A333489 onto the Barbelo Prime Tree (Barbelo & Claude, 2026, DOI: 10.5281/zenodo.20475174). In the prime tree, prime numbers form a vertical trunk and composite numbers branch alternately left and right between consecutive primes — like a fishbone structure. In this second visualization, all numbers belonging to sequence A333489 are additionally highlighted in magenta, regardless of whether they are prime or composite. A333489 contains all natural numbers k for which the k-th composition in standard order is an anti-run — meaning no two adjacent parts are equal. The composition is derived directly from the binary representation of k. The interactive interface supports zoom, pan, search, and a range slider from 2 to 1,000. Implemented in pure HTML5/Canvas with no external libraries. No comparable visualization of A333489 in a prime tree context is known to exist.
Barbelo et al. (Mon,) studied this question.