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R. L. Graham and H. O. Pollak observed that the sequence $$u_1=1,\qquadu_{n+1}=\lfloor \sqrt{2} (u_n+1/2)\rfloor, \quad n\geq 1,$$ has the curiousproperty that the sequence of numbers $(u_{2n+1}-2u_{2n-1})_{n\geq 1}$ denotesthe binary digits of $\sqrt{2}$. We present an extension of Graham--Pollak'ssequence which allows to get -- in a fancy way -- the binary digits of$759250125\sqrt{2}$ and other numbers.

A fancy way to obtain the binary digits of $759250125\sqrt{2}$