ocaml: phase 5.1 euler30_cube.ml baseline (sum of digit-cube narcissistic numbers <= 999 = 1301)

Numbers equal to the sum of cubes of their digits:
  153 = 1 + 125 + 27
  370 = 27 + 343 + 0
  371 = 27 + 343 + 1
  407 = 64 + 0 + 343
  sum = 1301

Implementation:
  pow_digit_sum n p   walk digits of n, accumulate d^p
  euler30 p limit     scan 2..limit and sum where pow_digit_sum n p = n

Real PE30 uses 5th powers (answer 443839); the cube version
exercises the same algorithm in a smaller search space.

118 baseline programs total.

lib/ocaml/baseline/euler30_cube.ml

@@ -0,0 +1,22 @@
+let pow_digit_sum n p =
+  let m = ref n in
+  let s = ref 0 in
+  while !m > 0 do
+    let d = !m mod 10 in
+    let pd = ref 1 in
+    for _ = 1 to p do pd := !pd * d done;
+    s := !s + !pd;
+    m := !m / 10
+  done;
+  !s
+
+let euler30 p limit =
+  let total = ref 0 in
+  for n = 2 to limit do
+    if pow_digit_sum n p = n then total := !total + n
+  done;
+  !total
+
+;;
+
+euler30 3 999

lib/ocaml/baseline/expected.json

@@ -32,6 +32,7 @@
   "euler2.ml": 4613732,
   "euler25.ml": 55,
   "euler28.ml": 261,
+  "euler30_cube.ml": 1301,
   "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 — euler30_cube.ml baseline (sum of numbers
+  equal to sum of cubes of their digits, ≤999 = 1301). The full
+  numbers are 153 + 370 + 371 + 407 = 1301. PE30 proper uses 5th
+  powers (answer 443839); cube version exercises the same algorithm
+  in a smaller search space. 118 baseline programs total.
 - 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