Distribution of 0 digits in factorial series: Difference between revisions

import java.math.BigInteger;

import java.util.List;

public final class DistributionInFactorials {

public static void main(String[] aArgs) {

List<Integer> limits = List.of( 100, 1_000, 10_000 );

for ( Integer limit : limits ) {

meanFactorialDigits(limit);

}

}

private static void meanFactorialDigits(Integer aLimit) {

BigInteger factorial = BigInteger.ONE;

double proportionSum = 0.0;

double proportionMean = 0.0;

for ( int n = 1; n <= aLimit; n++ ) {

factorial = factorial.multiply(BigInteger.valueOf(n));

String factorialString = factorial.toString();

int digitCount = factorialString.length();

long zeroCount = factorialString.chars().filter( ch -> ch == '0' ).count();

proportionSum += (double) zeroCount / digitCount;

proportionMean = proportionSum / n;

}

String result = String.format("%.8f", proportionMean);

System.out.println("Mean proportion of zero digits in factorials from 1 to " + aLimit + " is " + result);

}

}

Mean proportion of zero digits in factorials from 1 to 100 is 0.24675319

Mean proportion of zero digits in factorials from 1 to 1000 is 0.20354455

Mean proportion of zero digits in factorials from 1 to 10000 is 0.17300385