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Claim. Let $w>0$, $t=w/2^{\lfloor\log_2w\rfloor}$, $a=2(1-1/(t+2))$ and $b=2/a$. The recurrence $u_1=1$, $u_{n+1}=\lfloor a(u_n+1/2)\rfloor$ for odd $n$ and $u_{n+1}=\lfloor b(u_n+1/2)\rfloor$ for even $n$ has $u_{2n+1}-2u_{2n-1}$ equal to the $n$th digit in the binary expansion of $w$. At $w=\sqrt2$ it gives $a=b=\sqrt2$, the Graham--Pollak recurrence of Problem 482. The paper is not held: the statement is taken from Stoll's restatement of it as Theorem 1.1 of Stoll 2005 which reports that Rabinowitz and Gilbert found the values of $a$ and $b$ by a computational guessing approach and that their paper closes by asking for a ternary analog.

Covers. Recurrences of the Graham--Pollak shape that read the binary digits of every positive real $w$, so of every $\sqrt m$ and every positive algebraic number, in one binary family. Stoll's theorems, on the accepted full claim beside this page, extend it to infinitely many families and to every base $g\ge2$; Case I of Stoll's Theorem 1.2 at $j=1$ is this family.

Acceptance. Refereed: S. Rabinowitz and P. Gilbert, A nonlinear recurrence yielding binary digits, Math. Mag. 64 (1991), no. 3, 168--171. Stoll's 2006 paper (Acta Arith. 125, p. 90) counts it among the partial results on the problem. The site's curator does not credit it, so no reviewed evidence is listed. Boris Alexeev's repository, linked above, holds a third-party Lean proof of the family whose header names Rabinowitz and Gilbert among its informal authors and Codex and GPT-5.6 Sol as its formal authors; it was not built here, so no formalized evidence is listed. The page is dated to the June 1991 issue, which prints no fuller date.