How to save previous calculation

Question

I want to calculate the longest chain up on million applying repetily the Collatz function until it reach one.

I was able to solve this using the following code:

This is the definition of the function:

 Co[n_Integer] := If[EvenQ[n], n/2, 3 n + 1];

How to calculate the lenght of the chain:

Rco[m_Integer] := Module[{n = m},
      A = {};
      While[Co[n] != 1,
       A = Join[A, {Co[n]}];
       n = Co[n];
       ];
      Join[A, {1}]
      ]

and this last piece of code that calculate the lenght of everything and take the longest

Last[SortBy[Table[{Length[Rco[n]], n}, {n, 1, 1000000}], #[[1]] &]]

This is clearly a very wasteful way to compute such a lenght. Indeed my computer took several minutes to do it.

I know that since the these chains depend at some point of previus chains I could use previus calculation to reduce the amount of work my computer has to use. But I do not know how to this.

Thanks in advance.

Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. — Ben Izd, Jul 09 '21 at 17:59
The simplest form for saving previous results would be fn[x]:=fn[x]=code. Also for your first function, I encourage you to read Applying Functions Repeatedly. — Ben Izd, Jul 09 '21 at 18:04
also see this answer for more info on the memoization mentioned by Ben Izd! — thorimur, Jul 09 '21 at 22:23

How to save previous calculation

0 Answers0