p44.erl

-module(p44).

-export([answer/0]).

%% Pentagonal numbers are generated by the formula, P(n)=n(3n−1)/2. The first ten pentagonal numbers are:
%% 1,5,12,22,35,51,70,92,117,145, ...
%% It can be seen that P(4) + P(7) = 22 + 70 = 92 = P(8). However, their difference, 70 − 22 = 48, is not pentagonal.
%% Find the pair of pentagonal numbers, P(j) and P(k), for which their sum and difference is pentagonal and D = |P(k) − P(j)| is minimised;
%% what is the value of D?

-compile(export_all).

answer() ->
    [P | Ps] = [penta(N) || N <- lists:seq(2,2400)],
    find_diff(P, Ps, 1000000000).

find_diff(_, [], Diff) -> Diff;
find_diff(J, Ps, Diff) ->
    Ks = lists:filter(fun(K) ->
                              lists:member(J+K, Ps) andalso lists:member(K-J, Ps)
                      end, Ps),
    Diff1 = lists:foldl(fun(K, D) ->
                                case abs(J-K) < D of
                                    true -> abs(J-K);
                                    false -> D
                                end
                        end, Diff, Ks),
    find_diff(hd(Ps), tl(Ps), Diff1).

penta(N) -> N * ( 3 * N - 1 ) div 2.