{"schema":"vela.problem-packet.v0.1","problem":482,"statement":"Define a sequence by $a_1=1$ and\\[a_{n+1}=\\lfloor\\sqrt{2}(a_n+1/2)\\rfloor\\]for $n\\geq 1$. The difference $a_{2n+1}-2a_{2n-1}$ is the $n$th digit in the binary expansion of $\\sqrt{2}$.Find similar results for $\\theta=\\sqrt{m}$, and other algebraic numbers.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A004539","name":"Expansion of sqrt(2) in base 2.","terms":"1,0,1,1,0,1,0,1,0,0,0,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,0,","url":"https://oeis.org/A004539"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}