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Ross, KA (2012)

First Digits of Squares and Cubes

Mathematics Magazine 85(1), 36-42.

ISSN/ISBN: Not available at this time. DOI: 10.4169/math.mag.85.1.36

Abstract: Benford’s Law is the observation that in many lists of numbers that arise in the real world, for d = 1, 2, …, 9, the likelihood that the first digit is d is log10 ((d + 1)/d). A similar phenomenon is known for essentially all geometric sequences ark, namely the relative frequencies RN(d) of the first digit d of the first N terms in such a sequence tend to log10((d + 1)/d). In this note, it is shown that the analogous statements for the sequence of squares and the sequence of cubes do not hold. However, in these cases, interesting subsequences of RN(d) do converge, but not to log10((d + 1)/d).

@article {, AUTHOR = {Kenneth A. Ross}, TITLE = {First Digits of Squares and Cubes}, JOURNAL = {Mathematics Magazine}, VOLUME = {85}, NUMBER = {1}, YEAR = {2012}, PAGES = {36--42}, DOI = {10.4169/math.mag.85.1.36}, }

Reference Type: Journal Article

Subject Area(s): Analysis, General Interest