# Nested List Product

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.

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For what it's worth your original version is faster than the answers provided. – Mr.Wizard Jan 10 '13 at 7:28
@Mr.Wizard my original version is incomplete so I asked how to combine them at once and also how to have access to them once they're computed not at the end. No answer yet. – Mohsen Afshin Jan 10 '13 at 8:21
I didn't understand this part: "I want to be able to use each element once computed." Could you give an example of what you mean? – Mr.Wizard Jan 10 '13 at 9:35
@Mr.Wizard, it is an iterative computation, as an example when 2*3 => 6 and then 6*35 => 210 I want have access (a simple Print here) to both 6 and 35 in the middle of computation not at the end and using [[]] over the list. – Mohsen Afshin Jan 10 '13 at 11:33

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}} *)

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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]

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