Project Euler #44

44.ml

#load "euler.cma";;

open Euler;;

let pentagonal n = n * (3*n - 1) / 2;;

let pentagonal_index n = int_of_float ((1. +. sqrt(1. +. 24. *. float_of_int(n))) /. 6.);;

let is_pentagonal d = (mod_float ((sqrt(24. *. float_of_int(d) +. 1.) +. 1.) /. 6.) 1.) = 0.;;

let get_pentagonals n = List.rev_map (pentagonal) (range n);;

let low_pentagonals n =
  let idx = pentagonal_index n in
    get_pentagonals (idx-1);;

let rec search_pentagonal l = match l with
    [] -> raise Not_found
  | h :: t ->
      let low = low_pentagonals h in
      let sums = List.filter (fun x -> is_pentagonal (h + x)) low in
      let good = List.filter (fun x -> is_pentagonal (h - x)) sums in
        if List.length good > 0 then
          (h, good)
        else
          search_pentagonal t;;

let _ = 
  let r = search_pentagonal (get_pentagonals 3000) in
  let num = fst(r) in
  let list = snd(r) in
    List.rev_map (fun x -> Printf.printf "%d\n" x) (List.rev_map (fun x -> num - x) list)