Nested List Product

Question

I want to apply Times on the elements of a list such that:

{2,3,5,7,11,13,17,19} => 
{{2,3,5,7,11,13,17,19},{6,35,143,323},{210,46189},{9699690}}

I wrote this function :

listProduct[list_] := 
 Apply[Times, Partition[list, Ceiling[Length[list]/2]]]

Nest[listProduct, {2, 3, 5, 7, 11, 13, 17, 19}, 1]

Using Nest at each level generate the desired element but I am having difficulties with combining the results. Also, I want to be able to use each element once computed.

Answer 1

You can do :

listProduct2[list_] := Times @@@ Partition[list, 2, 2]

NestList[listProduct2, {2, 3, 5, 7, 11, 13, 17, 19}, 3]
(* {{2, 3, 5, 7, 11, 13, 17, 19}, {6, 35, 143, 323}, {210, 46189}, {9699690}} *)

Answer 2

If you don't want to count how often you have to call the function, you can use FixedPointList which automatically stops when there is nothing more to multiply

FixedPointList[
 Times @@@ Partition[#, 2, 2] &, {2, 3, 5, 7, 11, 13, 17, 19}]
(*
{{2, 3, 5, 7, 11, 13, 17, 19}, {6, 35, 143, 323}, {210, 46189}, 
 {9699690}, {}, {}}
*)

To get rid of the last two empty lists you can use Drop[..,-2]