Initial data commit

Task/EKG-sequence-convergence/Nim/ekg-sequence-convergence.nim

@@ -0,0 +1,43 @@
+import algorithm, math, sets, strformat, strutils
+
+#---------------------------------------------------------------------------------------------------
+
+iterator ekg(n, limit: Positive): (int, int) =
+  var values: HashSet[int]
+  doAssert n >= 2
+  yield (1, 1)
+  yield (2, n)
+  values.incl(n)
+  var i = 3
+  var prev = n
+  while i <= limit:
+    var val = 2
+    while true:
+      if val notin values and gcd(val, prev) != 1:
+        values.incl(val)
+        yield (i, val)
+        prev = val
+        break
+      inc val
+    inc i
+
+#---------------------------------------------------------------------------------------------------
+
+for n in [2, 5, 7, 9, 10]:
+  var result: array[1..10, int]
+  for i, val in ekg(n, 10): result[i] = val
+  let title = fmt"EKG({n}):"
+  echo fmt"{title:8} {result.join("", "")}"
+
+var ekg5, ekg7: array[1..100, int]
+for i, val in ekg(5, 100): ekg5[i] = val
+for i, val in ekg(7, 100): ekg7[i] = val
+var convIndex = 0
+for i in 2..100:
+  if ekg5[i] == ekg7[i] and sorted(ekg5[1..<i]) == sorted(ekg7[1..<i]):
+    convIndex = i
+    break
+if convIndex > 0:
+  echo fmt"EKG(5) and EKG(7) converge at index {convIndex}."
+else:
+  echo "No convergence found in the first {convIndex} terms."