Problem 44

44.c

@@ -0,0 +1,56 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdbool.h>
+#include <math.h>
+
+int try = 3000;
+int* pentagonalTable;
+int* pentagonals;
+
+bool isPentagonal (int n) {
+    if (n < try && pentagonalTable[n] == -1)
+        return false;
+    if (n < try && pentagonalTable[n] == 1)
+        return true;
+    else {
+        int radicand = 24*n + 1;
+        int sqrtr = sqrt (radicand);
+        if (sqrtr * sqrtr == radicand && (sqrtr + 1) % 6 == 0) {
+            if (n < try)
+                pentagonalTable[n] = 1;
+            return true;
+        }
+        else {
+            if (n < try)
+                pentagonalTable[n] = -1;
+            return false;
+        }
+    }
+}
+
+int pentagonalize (int n) {
+    if (n < try) {
+        if (pentagonals[n] == 0) {
+            pentagonals[n] = n * (3*n - 1) / 2;
+            if (pentagonals[n] < try)
+                pentagonalTable[pentagonals[n]] = 1;
+        }
+        return pentagonals[n];
+    }
+    else
+        return n * (3*n - 1) / 2;
+}
+
+int main () {
+    pentagonalTable = calloc (try, sizeof (int));
+    pentagonals = calloc (try, sizeof (int));
+    for (int j = 1; j < try; j++) {
+        for (int k = 1; k < j; k++) {
+            int pj = pentagonalize (j);
+            int pk = pentagonalize (k);
+            if (isPentagonal (pj + pk) && isPentagonal (pj - pk)) {
+                printf ("j: %d; k: %d; Pj: %d; Pk: %d; D: %d", j, k, pj, pk, pj - pk);
+            }
+        }
+    }
+}