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The Pell Tower and Ostronometry
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patternsbi-infiniteconsiderationsconsideredconwaydefineddiscoveredexotic
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Conway and Ryba considered a table of bi-infinite Fibonacci sequences and discovered new interesting patterns. We extend their considerations to tables that are defined by the recurrence $X_{n+1}=dX_n+X_{n-1}$ for natural numbers $d$. In our search for new patterns we run into a Red Wall and exotic numeration systems.
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Cited by 1 Pith paper
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Beatty solutions of almost Golomb equations
The almost Golomb equation of order r admits inhomogeneous Beatty sequence solutions of slope 1/sqrt(r) for r not an even perfect square, plus a one-parameter family obtained by composing the equation with itself.
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