diff -r 135bf034ac30 -r 6a77c260c8a5 core_testing1/collatz.scala
--- a/core_testing1/collatz.scala	Wed Nov 01 15:01:32 2023 +0000
+++ b/core_testing1/collatz.scala	Thu Nov 02 11:32:10 2023 +0000
@@ -1,33 +1,27 @@
-import scala.annotation.tailrec
 // Core Part 1 about the 3n+1 conjecture
 //============================================
 
 object C1 {
 
-@tailrec
-private def collatz(n: Long, steps: Long = 0): Long = {
-  if (n == 1) steps
-  else if (n % 2 == 0) collatz(n / 2, steps + 1)
-  else collatz(n * 3 + 1, steps + 1)
-}
-
-def collatz_max(upper: Long): (Long, Long) = {
-  (1L to upper).map(n => (collatz(n), n)).maxBy(_._1)
-}
+def collatz(n: Long): Long =
+  if (n == 1) 0 else
+    if (n % 2 == 0) 1 + collatz(n / 2) else 
+      1 + collatz(3 * n + 1)
 
 
-private def is_pow_of_two(n: Long) : Boolean = {
-  (n & (n - 1)) == 0
+def collatz_max(bnd: Long): (Long, Long) = {
+  val all = for (i <- (1L to bnd)) yield (collatz(i), i)
+  all.maxBy(_._1)
 }
 
-private def is_hard(n: Long) : Boolean = {
-  is_pow_of_two(3 * n + 1)
-}
+def is_pow(n: Long) : Boolean = (n & (n - 1)) == 0
+
+def is_hard(n: Long) : Boolean = is_pow(3 * n + 1)
 
-
-private def last_odd(n: Long): Long = {
-  (1L to n).filter(is_hard).max
-}
+def last_odd(n: Long) : Long = 
+  if (is_hard(n)) n else
+    if (n % 2 == 0) last_odd(n / 2) else 
+      last_odd(3 * n + 1)
 
 }