Data update

Task/EKG-sequence-convergence/JavaScript/ekg-sequence-convergence.js

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+// Calculate and show here the first 10 members of EKG[2], EKG[5], EKG[7], EKG[9] and EKG[10]
+for (const i of [2, 5, 7, 9, 10]) {
+    console.log(`EKG[${i}] = [${ekg(i, 10).join(', ')}]`);
+}
+
+console.log("Calculate and show here at which term EKG[5] and EKG[7] converge.");
+const ekg5 = ekg(5, 100);
+const ekg7 = ekg(7, 100);
+
+for (let i = 1; i < ekg5.length; i++) {
+    if (ekg5[i] === ekg7[i] && sameSeq(ekg5, ekg7, i)) {
+        console.log(`EKG[5](${i + 1}) = EKG[7](${i + 1}) = ${ekg5[i]}, and are identical from this term on`);
+        break;
+    }
+}
+
+// Same last element, and all elements in sequence are identical
+function sameSeq(seq1, seq2, n) {
+    const list1 = seq1.slice(0, n).sort((a, b) => a - b);
+    const list2 = seq2.slice(0, n).sort((a, b) => a - b);
+
+    for (let i = 0; i < n; i++) {
+        if (list1[i] !== list2[i]) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// Without Map to identify seen terms, need to examine list.
+//   Calculating 3000 terms in this manner takes 10 seconds
+// With Map to identify the seen terms, calculating 3000 terms takes .1 sec.
+function ekg(two, maxN) {
+    const result = [];
+    result.push(1);
+    result.push(two);
+
+    const seen = new Map();
+    seen.set(1, 1);
+    seen.set(two, 1);
+
+    let minUnseen = two === 2 ? 3 : 2;
+    let prev = two;
+
+    for (let n = 3; n <= maxN; n++) {
+        let test = minUnseen - 1;
+        while (true) {
+            test++;
+            if (!seen.has(test) && gcd(test, prev) > 1) {
+                result.push(test);
+                seen.set(test, n);
+                prev = test;
+
+                if (minUnseen === test) {
+                    do {
+                        minUnseen++;
+                    } while (seen.has(minUnseen));
+                }
+                break;
+            }
+        }
+    }
+    return result;
+}
+
+function gcd(a, b) {
+    if (b === 0) {
+        return a;
+    }
+    return gcd(b, a % b);
+}