ocaml: phase 5.1 euler28.ml baseline (sum of diagonals in 7x7 spiral = 261)

For each layer 1..(n-1)/2, the four corners of an Ulam spiral are
spaced 2*layer apart. Step k four times per layer, accumulate:

  let euler28 n =
    let s = ref 1 in
    let k = ref 1 in
    for layer = 1 to (n - 1) / 2 do
      let step = 2 * layer in
      for _ = 1 to 4 do
        k := !k + step;
        s := !s + !k
      done
    done;
    !s

  euler28 7 = 1 + (3+5+7+9) + (13+17+21+25) + (31+37+43+49) = 261

Real PE28 uses 1001x1001 (answer 669171001); 7x7 is fast.

117 baseline programs total.

lib/ocaml/baseline/euler28.ml

@@ -0,0 +1,15 @@
+let euler28 n =
+  let s = ref 1 in
+  let k = ref 1 in
+  for layer = 1 to (n - 1) / 2 do
+    let step = 2 * layer in
+    for _ = 1 to 4 do
+      k := !k + step;
+      s := !s + !k
+    done
+  done;
+  !s
+
+;;
+
+euler28 7

lib/ocaml/baseline/expected.json

@@ -31,6 +31,7 @@
   "euler14.ml": 97,
   "euler2.ml": 4613732,
   "euler25.ml": 55,
+  "euler28.ml": 261,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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.
+- 2026-05-09 Phase 5.1 — euler28.ml baseline (sum of diagonals in
+  7x7 number spiral = 261). For each layer (1..(n-1)/2) the four
+  corners are spaced 2*layer apart, so we step `k` four times per
+  layer and accumulate into s. Real PE28 uses 1001x1001 (answer
+  669171001); 7x7 is fast enough to land in seconds. 117 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — euler14.ml baseline (longest Collatz chain
   starting under N=100 → 97). collatz_len walks n through the
   iteration n/2 if even, 3n+1 if odd, counting steps. Outer loop