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ConvergentsOfE.java
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ConvergentsOfE.java
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package dev;
import java.math.BigInteger;
import java.util.function.Function;
public class ConvergentsOfE {
public static void main(String[] args) {
BigInteger[] convergent = getConvergent(100);
System.out.println("Numerator of 100th convergent: " + convergent[0]);
System.out.println("Sum of digits in the numerator of 100th convergent: " + sumOfDigits(convergent[0]));
}
private static BigInteger[] getConvergent(int n) {
BigInteger h0 = BigInteger.valueOf(2);
BigInteger h1 = BigInteger.valueOf(3);
BigInteger k0 = BigInteger.ONE;
BigInteger k1 = BigInteger.ONE;
Function<Integer, BigInteger> a = (k) -> {
if (k == 0) return BigInteger.valueOf(2);
if (k % 3 == 2) return BigInteger.valueOf(2 * (k / 3 + 1));
return BigInteger.ONE;
};
for (int i = 2; i < n; i++) {
BigInteger hi = a.apply(i).multiply(h1).add(h0);
BigInteger ki = a.apply(i).multiply(k1).add(k0);
h0 = h1;
h1 = hi;
k0 = k1;
k1 = ki;
}
return new BigInteger[]{h1, k1};
}
private static int sumOfDigits(BigInteger number) {
String digits = number.toString();
int sum = 0;
for (int i = 0; i < digits.length(); i++) {
sum += Character.digit(digits.charAt(i), 10);
}
return sum;
}
}