(*

* Solution to Project Euler problem 44

* Copyright (c) Project Nayuki. All rights reserved.

*

* https://www.nayuki.io/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*)

PentaNumber[x_] := x * (x * 3 - 1) / 2

PentaNumberQ[y_] := y > 0 && Block[{z = Sqrt[y * 24 + 1]}, IntegerQ[z] && Mod[z, 6] == 5]

minD = -1; (* -1 means not found yet, positive number means found a candidate *)

(* For each upper pentagonal number index, going upward *)

For[i = 2, True, i++,

pentI = PentaNumber[i];

(* If the next number down is at least as big as a found difference, then conclude searching *)

If[minD != -1 && pentI - PentaNumber[i - 1] >= minD,

Break[]];

(* For each lower pentagonal number index, going downward *)

For[j = i - 1, j >= 1, j--,

pentJ = PentaNumber[j];

diff = pentI - pentJ;

(* If the difference is at least as big as a found difference, then stop testing lower pentagonal numbers *)

If[minD != -1 && diff >= minD,

Break[]];

If[PentaNumberQ[pentI + pentJ] && PentaNumberQ[diff],

minD = diff]]]

minD