Data commit

Task/Sphenic-numbers/Java/sphenic-numbers.java

@@ -0,0 +1,113 @@
+import java.util.Arrays;
+import java.util.ArrayList;
+import java.util.List;
+
+public class SphenicNumbers {
+    public static void main(String[] args) {
+        final int limit = 1000000;
+        final int imax = limit / 6;
+        boolean[] sieve = primeSieve(imax + 1);
+        boolean[] sphenic = new boolean[limit + 1];
+        for (int i = 0; i <= imax; ++i) {
+            if (!sieve[i])
+                continue;
+            int jmax = Math.min(imax, limit / (i * i));
+            if (jmax <= i)
+                break;
+            for (int j = i + 1; j <= jmax; ++j) {
+                if (!sieve[j])
+                    continue;
+                int p = i * j;
+                int kmax = Math.min(imax, limit / p);
+                if (kmax <= j)
+                    break;
+                for (int k = j + 1; k <= kmax; ++k) {
+                    if (!sieve[k])
+                        continue;
+                    assert(p * k <= limit);
+                    sphenic[p * k] = true;
+                }
+            }
+        }
+
+        System.out.println("Sphenic numbers < 1000:");
+        for (int i = 0, n = 0; i < 1000; ++i) {
+            if (!sphenic[i])
+                continue;
+            ++n;
+            System.out.printf("%3d%c", i, n % 15 == 0 ? '\n' : ' ');
+        }
+
+        System.out.println("\nSphenic triplets < 10,000:");
+        for (int i = 0, n = 0; i < 10000; ++i) {
+            if (i > 1 && sphenic[i] && sphenic[i - 1] && sphenic[i - 2]) {
+                ++n;
+                System.out.printf("(%d, %d, %d)%c",
+                                  i - 2, i - 1, i, n % 3 == 0 ? '\n' : ' ');
+            }
+        }
+
+        int count = 0, triplets = 0, s200000 = 0, t5000 = 0;
+        for (int i = 0; i < limit; ++i) {
+            if (!sphenic[i])
+                continue;
+            ++count;
+            if (count == 200000)
+                s200000 = i;
+            if (i > 1 && sphenic[i - 1] && sphenic[i - 2]) {
+                ++triplets;
+                if (triplets == 5000)
+                    t5000 = i;
+            }
+        }
+
+        System.out.printf("\nNumber of sphenic numbers < 1,000,000: %d\n", count);
+        System.out.printf("Number of sphenic triplets < 1,000,000: %d\n", triplets);
+
+        List<Integer> factors = primeFactors(s200000);
+        assert(factors.size() == 3);
+        System.out.printf("The 200,000th sphenic number: %d = %d * %d * %d\n",
+                          s200000, factors.get(0), factors.get(1),
+                          factors.get(2));
+        System.out.printf("The 5,000th sphenic triplet: (%d, %d, %d)\n",
+                          t5000 - 2, t5000 - 1, t5000);
+    }
+
+    private static boolean[] primeSieve(int limit) {
+        boolean[] sieve = new boolean[limit];
+        Arrays.fill(sieve, true);
+        if (limit > 0)
+            sieve[0] = false;
+        if (limit > 1)
+            sieve[1] = false;
+        for (int i = 4; i < limit; i += 2)
+            sieve[i] = false;
+        for (int p = 3, sq = 9; sq < limit; p += 2) {
+            if (sieve[p]) {
+                for (int q = sq; q < limit; q += p << 1)
+                    sieve[q] = false;
+            }
+            sq += (p + 1) << 2;
+        }
+        return sieve;
+    }
+
+    private static List<Integer> primeFactors(int n) {
+        List<Integer> factors = new ArrayList<>();
+        if (n > 1 && (n & 1) == 0) {
+            factors.add(2);
+            while ((n & 1) == 0)
+                n >>= 1;
+        }
+        for (int p = 3; p * p <= n; p += 2) {
+            if (n % p == 0) {
+                factors.add(p);
+                while (n % p == 0)
+                    n /= p;
+            }
+        }
+        if (n > 1)
+            factors.add(n);
+        return factors;
+    }
+}