Data update

Task/Curzon-numbers/JavaScript/curzon-numbers.js

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+/**
+ * Curzon Numbers
+ *
+ * A generalized Curzon number is a positive integer n such that:
+ * k^n + 1 is divisible by (k * n + 1)
+ * For k = 2, this gives the classic definition of Curzon numbers
+ */
+
+function isGeneralisedCurzonNumber(aK, aN) {
+    const r = aK * aN;
+    return modulusPower(aK, aN, r + 1) === r;
+}
+
+function modulusPower(aBase, aExponent, aModulus) {
+    if (aModulus === 1) {
+        return 0;
+    }
+
+    aBase %= aModulus;
+    let result = 1;
+    while (aExponent > 0) {
+        if ((aExponent & 1) === 1) {
+            result = (result * aBase) % aModulus;
+        }
+        aBase = (aBase * aBase) % aModulus;
+        aExponent >>= 1;
+    }
+    return result;
+}
+
+function main() {
+    for (let k = 2; k <= 10; k += 2) {
+        console.log(`Generalised Curzon numbers with base ${k}:`);
+
+        let n = 1;
+        let count = 0;
+        const results = [];
+
+        // Find the first 50 Curzon numbers
+        while (count < 50) {
+            if (isGeneralisedCurzonNumber(k, n)) {
+                results.push(n);
+                count++;
+            }
+            n++;
+        }
+
+        // Print in rows of 10
+        for (let i = 0; i < results.length; i++) {
+            const lineEnd = (i + 1) % 10 === 0 ? '\n' : ' ';
+            process.stdout.write(`${results[i].toString().padStart(4)}${lineEnd}`);
+        }
+
+        // Reset and find the 1000th Curzon number
+        count = 0;
+        while (count < 1000) {
+            if (isGeneralisedCurzonNumber(k, n)) {
+                count++;
+            }
+            n++;
+        }
+
+        console.log(`1,000th Generalised Curzon number with base ${k}: ${n - 1}`);
+        console.log();
+    }
+}
+
+main();