ocaml: phase 5.1 euler34_small.ml baseline (factorions <= 2000 = 145)

Number that equals the sum of factorials of its digits:
  145 = 1! + 4! + 5! = 1 + 24 + 120

Implementation:
  fact n           iterative factorial
  digit_fact_sum n walk digits, sum fact(digit)
  euler34 limit    scan 3..limit, accumulate matches

The only other factorion is 40585 = 4!+0!+5!+8!+5!. Real PE34 sums
both (= 40730); 2000 keeps under our search budget.

121 baseline programs total.

lib/ocaml/baseline/euler34_small.ml

@@ -0,0 +1,24 @@
+let fact n =
+  let r = ref 1 in
+  for i = 2 to n do r := !r * i done;
+  !r
+
+let digit_fact_sum n =
+  let m = ref n in
+  let s = ref 0 in
+  while !m > 0 do
+    s := !s + fact (!m mod 10);
+    m := !m / 10
+  done;
+  !s
+
+let euler34 limit =
+  let total = ref 0 in
+  for n = 3 to limit do
+    if digit_fact_sum n = n then total := !total + n
+  done;
+  !total
+
+;;
+
+euler34 2000

lib/ocaml/baseline/expected.json

@@ -35,6 +35,7 @@
   "euler28.ml": 261,
   "euler29_small.ml": 15,
   "euler30_cube.ml": 1301,
+  "euler34_small.ml": 145,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,

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.
+- 2026-05-09 Phase 5.1 — euler34_small.ml baseline (numbers equal
+  to sum of factorials of digits, ≤2000 = 145). 145 = 1!+4!+5! =
+  1+24+120. The other "factorion" 40585 is the only number above
+  this threshold; PE34 sums both = 40730. 121 baseline programs
+  total.
 - 2026-05-09 Phase 5.1 — euler29_small.ml baseline (distinct a^b for
   2≤a,b≤5 = 15). 16 powers minus the one duplicate (4^2 = 2^4 = 16)
   → 15 distinct values. Hashtbl as a set with unit-payload (the