Material Detail

This app examines the first-digit distribution of various sequences: Additive, Power, and Prime Number

Additive Sequence: Consider a sequence of numbers where we fix the initial two numbers and then the value of each subsequent number is the sum of the previous two. We will call this an additive sequence. When the initial two numbers are both 1 then this yields the famous Fibonacci sequence. If you only consider the first digit of each number in an additive sequence and examine its distribution, is it the case that it closely follows Benford's Law? This app generates an additive sequence, for a given length and initial sequence numbers, and applies a goodness of fit test of the observed frequencies of first digits to Benford's Law.

Power Sequence: Consider a sequence of the form b¹, b², …, bⁿ, where b is called the base. We will call this a power sequence. If you only consider the first digit of each number in a power sequence and examine its distribution, is it the case that it closely follows Benford's Law? This app generates the power sequence, for a given b and n, and applies a goodness of fit test of the observed frequencies of first digits to Benford's Law.

Prime Number Sequence: Consider the sequence of prime numbers less than or equal to some power of 10. An article from 2009 shows that the distribution of the first digit of these prime numbers is well described by what's known as Generalized Benford's Law (GBL) . This app generates the prime numbers less than or equal to 10³, 10⁴, 10⁵, or 10⁶ and applies a goodness of fit test of the observed frequencies of first digits to GBL.

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