http://redd.it/2y5ziw

AdditionChains.ahk

#NoEnv
SetBatchLines, -1

Input := "13 743"

Start := A_TickCount
for each, Link in FindChain([2, 1], StrSplit(Input, " ")*)
	Out .= ", " Link
Elapsed := A_TickCount - Start
MsgBox, % SubStr(Out, 3) "`n" Elapsed "ms"

FindChain(Chain, Length, Num)
{
	if Chain.MaxIndex()-1 == Length
		return (Chain[1] == Num) ? Chain : False
	Performed := []
	Biggest := Chain[1]
	for each, BestLink in Chain
	{
		for each, Link in Chain
		{
			Sum := BestLink + Link
			if (Sum <= Biggest || Sum > Num || Performed[Sum]) ; The chain only ever increases, we don't want to decrease or go over
				continue
			Performed[Sum] := True
			if (Result := FindChain([Sum, Chain*], Length, Num))
				return Result
		}
	}
}