International Journal of Mathematics and Mathematical Sciences / 2009 / Article / Tab 3

Research Article

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

Table 3

Fitting integer sequences to the Benford and generalized Benford distributions

Name of sequenceSample sizeBenfordTwosided Power BenfordPareto Benford

chi-square -valuechi-square -value chi-square -value

Square1009.09633.437.83734.720.36299.91
Cube5009.69628.705.80856.230.28699.96
Cube100046.4590.0043.7250.000.4899.81
Cube10000443.7450.00472.0110.003.13879.13
Square root998.61237.617.00242.862.77883.61
Prime < 100257.74145.917.29939.841.84993.30
Prime < 100016845.0160.0036.6510.000.33399.93
Prime < 100001229387.1940.00307.3220.003.29777.07
Princeton number253.45290.292.76289.721.30297.16
Mixing sequence61815.5504.939.01425.171.81993.55
Pentagonal number1005.27772.762.12795.241.96892.26
Keith number719.21532.457.68836.097.40228.53
Bell number1003.06993.003.01488.372.60785.63
Catalan number1002.40496.612.30494.111.93492.57
Lucky number457.69346.405.16563.985.56447.37
Ulam number446.35060.812.52092.562.52686.56
Numeri ideoni652.59495.722.52292.542.58485.89
Fibonacci number1001.02999.811.02199.451.02798.46
Partition number941.39499.431.13299.241.51395.86