Why every sequence ⌊ξ(7/5)n⌋ has infinitely many composite terms — proved by building one finite graph and pruning it until nothing is left.
This animation explains the one-step method from the paper Finite graph certificates for composite terms in rational floor sequences by Yuri Odagiri (Section 3 and Section 5.1): the proof that for every real ξ > 0, infinitely many terms of ⌊ξ(7/5)n⌋ are divisible by 2, 3, 5, 11 or 13, and hence composite.
The graphs from Chapter 3 on are not pictures of pre-computed results: the page runs the one-step computation each time it opens (30,720 states at the first stage), and its counts agree with Tables 1 and 2 of the paper.
The narration was generated with Gemini 3.8 Flash TTS and plays in sync with the captions. It starts in a window-filling view; W switches to the page view with the chapter list, and F uses the whole screen. If the audio file cannot be loaded (for example when the HTML file is opened on its own), the browser's speech synthesis reads the captions instead.
Paper: DOI 10.5281/zenodo.22997709 · Sources and reproduction: github.com/ixixi/rational-floor-certificates · 日本語版 · Japanese explainer (chapters 1–3)