ocaml: phase 5.1 base_n.ml baseline (int to base-N string, length sum = 17)

36-character digit alphabet '0..9A..Z' supports any base 2..36. Loop
divides the magnitude by base and prepends the digit:

  while !m > 0 do
    acc := String.make 1 digits.[!m mod base] ^ !acc;
    m := !m / base
  done

Special-cases n = 0 -> '0' and prepends '-' for negatives.

Test cases (length, since the strings differ in alphabet):
  255 hex      'FF'              2
  1024 binary  '10000000000'    11
  100 dec      '100'             3
  0 any base   '0'               1
  sum                            17

Combines digits.[i] (string indexing) + String.make 1 ch + String
concatenation in a loop.

61 baseline programs total.

lib/ocaml/baseline/base_n.ml

@@ -0,0 +1,19 @@
+let to_base_n n base =
+  let digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" in
+  if n = 0 then "0"
+  else begin
+    let m = ref (abs n) in
+    let acc = ref "" in
+    while !m > 0 do
+      acc := String.make 1 digits.[!m mod base] ^ !acc;
+      m := !m / base
+    done;
+    if n < 0 then "-" ^ !acc else !acc
+  end
+
+;;
+
+String.length (to_base_n 255 16) +
+String.length (to_base_n 1024 2) +
+String.length (to_base_n 100 10) +
+String.length (to_base_n 0 16)

lib/ocaml/baseline/expected.json

@@ -8,6 +8,7 @@
   "bigint_add.ml": 28,
   "bits.ml": 21,
   "balance.ml": 3,
+  "base_n.ml": 17,
   "bfs.ml": 6,
   "btree.ml": 39,
   "brainfuck.ml": 75,

plans/ocaml-on-sx.md

@@ -407,6 +407,16 @@ _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 — base_n.ml baseline (int -> base-N string,
+  length sum 2+11+3+1 = 17). 36-character digit alphabet supports up
+  to base 36. Loop divides quotient by base, prepends digit. Tests:
+    255 hex     "FF"             2
+    1024 binary "10000000000"   11
+    100 dec     "100"            3
+    0 any base  "0"              1
+  Sum 17. Combines digits.[!m mod base] (string indexing) +
+  String.make 1 ch (1-char string from 1-char string in our model) +
+  String concatenation in a loop. 61 baseline programs total.
 - 2026-05-09 Phase 5.1 — prime_factors.ml baseline (trial-division
   factorisation, sum of factors of 360 = 17). Three refs threading
   through a while loop: m holds the remaining quotient, d the