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The fact that 09 is ahead so often is an example of the Arcsine Law Paradox at work. See for example Feller, Volume I, Chapter III. As Feller says, "[the conclusions] are not only unexpected but actually come as a shock to intuition and common sense." Of course the same phenomenon occurs with single digits of Pi, see A0096567, A096567, where 5 seems to be ahead most of the time. - N. J. A. Sloane, Mar 09 2023

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The fact that 09 is ahead so often is an example of the Arcsine Law Paradox at work. See for example Feller, Volume I, Chapter III. As Feller says, "[the conclusions] are not only unexpected but actually come as a shock to intuition and common sense." Of course the same phenomenon occurs with single digits of Pi, see A0096567, where 5 seems to be ahead most of the time. - N. J. A. Sloane, Mar 09 2023

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The fact that 09 is ahead so often is an example of the Arcsine Law Paradox at work. See for example Feller, Volume I, Chapter III. As Feller says, "[the conclusions] are not only unexpected but actually come as a shock to intuition and common sense." - N. J. A. Sloane, Mar 09 2023

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The fact that 09 is ahead so often is an example of the Arcsine Law Paradox at work. See for example Feller, Volume I, Chapter III. - N. J. A. Sloane, Mar 09 2023

William Feller, An Introduction to Probability Theory and Its Applications, Vol. I, Chapter III, Wiley, 3rd Ed., Corrected printing 1970.

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In the first 10000 terms we see "09" 40 times, "14" 33 times, and so on. Here is the complete list:

It does not mean that they do not appear in Pi. Indeed they do. It only means that they are never the first to reach some count. They may be behind by only a small amount. (End)

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