weirdest euler approximation based on https://twitter.com/AnalysisFact/status/961338838084878337

eulerapprox.java

public class WeirdEuler {
	public static int N = 1000000;
	
	public static double ak(int k) {
		if (k == 0) return 2;
		double product = 1;
		for (int i = k; i < 2*k; i+=2) {
			product *= ((double) (i+2)) / (i+1);
		}
		return Math.pow(product, 1.0 / k);
	}
	
	public static void main(String[] args) {
		double e = ak(0);
		for (int i = 2; i < N; i*=2) {
			e *= ak(i);
		}
		System.out.println(e);
	}
}