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To clarify, I mean every natural number base $b$ where $b \geq 2$. If so, what is the algorithm to generate the number (and what is the number, if it has a name)?

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Wikipedia reveals that the answer is yes, citing the paper "An example of a computable absolutely normal number" by Becher and Figueira (Theoretical Computer Science 270(1-2), 2002).

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    $\begingroup$ @Izzhov: It's hard to believe you've read that article in the time since I posted that link. But why would you be asking more questions before doing so? $\endgroup$ – Chris Eagle May 30 '13 at 18:25
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    $\begingroup$ I don't think you actually have to read the paper. It suffices to examine the title: "An example of a computable absolutely normal number" $\endgroup$ – Mark May 30 '13 at 18:26
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    $\begingroup$ Answers on this site are supposed to be self-contained. $\endgroup$ – MJD May 30 '13 at 18:32
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    $\begingroup$ I added the name and reference details of the paper so people can still find it if ScienceDirect changes their URLs in the future. $\endgroup$ – Rahul May 30 '13 at 18:43
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    $\begingroup$ @ChrisEagle Let me be more explicit: I had read B&F's paper before and I saw nowhere in it the value of the first bit $b_1$ of the normal number $b$ (despite the title of their section 3.1...). Hence I find rather odd the claim by the authors (copied on the WP page) that their algorithm indeed "generates" a number $b$. Before declaring that the answer to the OP question is "yes", at least some explanations about the meaning of some words used in B&F seem to be in order. $\endgroup$ – Did May 31 '13 at 11:01

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