International Journal of Mathematics and Mathematical Sciences / 2009 / Article / Tab 1

Research Article

Generalizing Benford's Law Using Power Laws: Application to Integer Sequences

Table 1

First digit distributions of some integer sequences.

Name of sequence Sample size Percentage of first digit occurrences

123456789

Benford law30.117.612.59.77.96.75.85.14.6
Square10021.014.012.012.09.09.08.07.08.0
Cube50028.214.811.49.88.87.86.66.85.8
Cube100022.615.912.410.69.48.37.47.16.3
Cube1000022.515.812.610.69.38.37.57.06.4
Square root9919.217.215.213.111.19.17.15.13.0
Prime < 1002516.012.012.012.012.08.016.08.04.0
Prime < 100016814.911.311.311.910.110.710.710.18.9
Prime < 10000122913.011.911.311.310.711.010.210.310.3
Princeton number2528.08.012.012.08.012.08.04.08.0
Mixing sequence61828.314.611.59.97.67.88.16.65.7
Pentagonal number10035.012.010.08.010.06.08.05.06.0
Keith number7132.414.114.17.04.27.012.72.85.6
Bell number10031.015.010.012.010.08.05.06.03.0
Catalan number10033.018.011.011.08.08.04.03.04.0
Lucky number4542.217.88.94.42.26.78.92.26.7
Ulam number4445.513.66.86.84.56.84.56.84.5
Numeri ideoni6530.818.513.810.86.23.17.76.23.1
Fibonacci number10030.018.013.09.08.06.05.07.04.0
Partition number9428.717.014.99.67.46.47.45.33.2

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.