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Experimental Mathematics Volume 23, 2014 - Issue 2
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Original Articles

The Decimal Expansion of π Is Not Statistically Random

Reinhard E. GanzSchweizerisches Epilepsie-Zentrum, Zürich, SwitzerlandCorrespondencereinhard.ganz@bluewin.ch
Pages 99-104 | Published online: 12 Jun 2014
 
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Abstract

This paper pursues the question whether the decimal expansion of π behaves as though it were the realization of a sequence of mutually independent, identically distributed random variables with uniform distribution on {0, 1, … , 9}. So far, no deviation from reasonable statistical norms has been found. We introduce an extended runs test of symbolic dynamics that π fails at a high level of statistical significance.

2000 AMS Subject Classification::

Notes

1Implementation from A. Fog, http://www.agner.org/random/ (download packages 2008–2010, version 2.01); GNU general public license.

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