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copied!<p>The other answers have explained why there's not an immediate infinite recursion issue (because generators are interpreted lazily). However, I think it is also interesting to consider when you might hit the finite limits on recursion that exist in the Python interpreter.</p> <p>First off, I noticed that your code can be simplified a bit (you've got a couple more functions than are really needed, and your <code>N</code> generator is identical to <code>itertools.count(1)</code>). So here's a simpler version of your generator:</p> <pre><code>from itertools import count def RZ(): x=count(1) y=RZ() while True: yield next(x) yield next(y) </code></pre> <p>Sample output:</p> <pre><code>>>> gen = RZ() >>> for i in range(1, 21): print i, next(gen) 1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1 9 5 10 3 11 6 12 2 13 7 14 4 15 8 16 1 17 9 18 5 19 10 20 3 </code></pre> <p>Next, I wrote a function that introspects into the nested generators and counts how deeply they have been evaluated. I'm not sure if this code is portable between python versions (I'm using 2.7):</p> <pre><code>def getDepth(gen): depth = 0 while gen: depth += 1 gen = gen.gi_frame.f_locals.get("y") return depth </code></pre> <p>Output from that (index, depth, value):</p> <pre><code>>>> for i in range(1, 21): print i, getDepth(gen), next(gen) 1 1 1 2 2 1 3 3 2 4 3 1 5 4 3 6 4 2 7 4 4 8 4 1 9 5 5 10 5 3 11 5 6 12 5 2 13 5 7 14 5 4 15 5 8 16 5 1 17 6 9 18 6 5 19 6 10 20 6 3 </code></pre> <p>Those depth values are growing logarithmically. Specifically, the depth of nested generators required to produce the Nth value of the sequence is <code>ceil(log(N, 2)) + 1</code>.</p> <p>In my copy of Python, recursion is allowed (by default) to go upto 100 levels deep. The generator will hit that limit only after 2^99 + 1 (=633,825,300,114,114,700,748,351,602,689) items have been produced. I wouldn't hold my breath waiting for that.</p>

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