Ah, good point, I should have thought about that. 1 was not the only
one I needed to concern myself with.
But I think it's this:
+/(0=1|3%:n)+.0=3|n
340
I think we can agree that 32^32 isn't a cube
32^32x
1461501637330902918203684832716283019655932542976
32 is 2^5 and 5*32 is 160, but 160 is not a multiple of 3, so 2^160 is
not perfect cube,
However,
(=<.)3%:32^32x
1
The problem here is that the cube root of
1461501637330902918203684832716283019655932542976 is too large to
represent the fractional part using floating point.
Still -- good catch.
Thanks,
--
Raul
On Sun, Mar 21, 2021 at 12:07 AM 'robert therriault' via Programming
<programm...@jsoftware.com> wrote:
>
> Thinking about it a bit further there are many more perfect cubes than that
> because integers such as 8^8 would not be captured by the %3 rule, but are
> still perfect cubes.
>
> My new answer which is certainly brute force.
>
> +/@:(=<.)@:(3&%:) n^n NB. take cube root of each n^n then set each
> one that is an integer to 1 and then total up the 1's in the list
> 985
> 100 timespacex '+/@:(=<.)@:(3&%:) n^n'
> 5.526e_5 29056
>
> Cheers, bob
>
> > On Mar 20, 2021, at 20:14, 'robert therriault' via Programming
> > <programm...@jsoftware.com> wrote:
> >
> > Same reasoning as Raul, but quicker and uses less space because we make use
> > of the structure of n
> >
> > (1 + [: <. 3 %~ {:) n
> > 334
> > 100 timespacex '1++//0=3 |n'
> > 2.69e_5 11200
> > 100 timespacex '(1 +[: <. 3 %~ {:) n'
> > 5.5e_7 1728
> >
> > Cheers, bob
> >
> >> On Mar 20, 2021, at 20:01, Raul Miller <rauldmil...@gmail.com> wrote:
> >>
> >> 1++/0=3 | n
> >> 334
> >>
> >> p is a perfect cube if n is 1 or if n is a multiple of 3.
> >>
> >> (1 is the only whole power of 3 which is not a multiple of 3.)
> >>
> >> FYI,
> >>
> >> --
> >> Raul
> >>
> >> On Sat, Mar 20, 2021 at 10:58 PM Skip Cave <s...@caveconsulting.com> wrote:
> >>>
> >>> How do you solve this problem using J (brute force)
> >>> n =. >: i. 1000
> >>> p =. n^n
> >>> How many p are perfect cubes?
> >>>
> >>> Skip Cave
> >>> Cave Consulting LLC
> >>> ----------------------------------------------------------------------
> >>> For information about J forums see http://www.jsoftware.com/forums.htm
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> >
> > ----------------------------------------------------------------------
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