ocaml: phase 5.1 josephus.ml baseline (n=50 k=3, survivor at position 11)

Classic Josephus problem solved with the standard recurrence:

  let rec josephus n k =
    if n = 1 then 0
    else (josephus (n - 1) k + k) mod n

  josephus 50 3 + 1 = 11

50 people stand in a circle, every 3rd is eliminated; the last
survivor is at position 11 (1-indexed). Tests recursion + mod.

136 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,11 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — josephus.ml baseline (Josephus problem,
+  n=50 k=3 → survivor at position 11, 1-indexed). Uses the classic
+  recursive formula: J(1, k) = 0; J(n, k) = (J(n-1, k) + k) mod n.
+  Returns 0-indexed survivor; we add 1 for human readability. Tests
+  recursion, mod, integer arithmetic. 136 baseline programs total.
 - 2026-05-10 Phase 5.1 — partition_count.ml baseline (number of
   integer partitions of 15 = 176). Classic DP: dp[0] = 1; for each
   k from 1..n, for each i from k..n, dp[i] += dp[i - k]. O(n²) time,