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pe044.ml
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pe044.ml
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open Core.Std
let is_pentagonal_number n =
let delta = 1 + 24 * n in
let root = (1. +. sqrt (Float.of_int delta)) /. 6. in
let root_int = Float.to_int root in
root_int * (3 * root_int - 1) / 2 = n ||
(root_int + 1) * (3 * root_int + 2) / 2 = n
let rec iter_diff cur =
let diff = cur * (3 * cur - 1) / 2 in
let rec iter pos_a pos_b =
let a = pos_a * (3 * pos_a - 1) / 2 in
let b = a + diff in
if (pos_b + 1) * (3 * pos_b + 2) / 2 <= b then
iter pos_a (pos_b + 1)
else
if pos_b * (3 * pos_b - 1) / 2 = b &&
is_pentagonal_number (a + b) then
Some b
else
if pos_a = pos_b then
None
else
iter (pos_a + 1) pos_b
in
match iter 1 cur with
| None -> iter_diff (cur + 1)
| Some _ -> diff
let () = iter_diff 1
|> Printf.printf "%d\n"