Abstract.The exact probability distribution of the first digit of integer powers up to an arbitrary but fixed number of digits is derived. Based on its asymptotic distribution, it is shown that it approaches Benford's law very closely for sufficiently high powers.

Received: October 15, 2003

AMS Subject Classification: 11B83, 11K31, 11Y55, 62E15, 62E20

Key Words and Phrases: integer sequence, powers, first digit, Benford's law, asymptotic distribution

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 11
Issue: 1