As usual you have a way of coming up with something brilliant that takes some time for me to understand.
I get it with the perfect squares and perfect cubes because that is what I was originally after but what has the perfect 6-th power to do with this? And by the way g3a gives me 86 and not 87 f3 =: - -/@:>.@:(2 6 3&%:) f3 87 75 g3a=: + -/@:>.@:(2 6 3&%:) g3a 75 86 2010/12/27 Roger Hui <rhui...@shaw.ca> > A fast inverse for f derives by observing that f is > equivalent to: > > f3 =: - -/@:>.@:(2 6 3&%:) > > That is, f3 n is n less the perfect squares and > perfect cubes bounded by n, plus the perfect 6-th > powers. The function g3a then is very near to the > inverse to f3 : > > g3a=: + -/@:>.@:(2 6 3&%:) > > For example: > > f3 1e9 > 999967409 > g3a 999967409 > 1000000000 > > However: > g3a 112 > 125 > f3 125 > 111 > > The details of deriving g3, the inverse for f3, are left > as an exercise for the reader. > > > > ----- Original Message ----- > From: Björn Helgason <gos...@gmail.com> > Date: Sunday, December 26, 2010 11:48 > Subject: [Jprogramming] finding number > To: Programming forum <programming@jsoftware.com> > > > I have a small task that looks like this > > > > f=: [: # i. -. (2 ^~ i.) , 3 ^~ i. > > f 87 > > 75 > > > > I want to use tacit to find what number gives me 75 numbers (the > > answerbeing 87) > > > > Could be asking what argument y do I need to find x numbers > > according to the > > formula above > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Björn Helgason, Verkfræðingur Fornustekkum II 781 Hornafirði, t-póst: gos...@gmail.com gsm: +3546985532 sími: +3544781286 http://groups.google.com/group/J-Programming Tæknikunnátta höndlar hið flókna, sköpunargáfa er meistari einfaldleikans góður kennari getur stigið á tær án þess að glansinn fari af skónum /|_ .-----------------------------------. ,' .\ / | Með léttri lund verður | ,--' _,' | Dagurinn í dag | / / | Enn betri en gærdagurinn | ( -. | `-----------------------------------' | ) | (\_ _/) (`-. '--.) (='.'=) ♖♘♗♕♔♙ `. )----' (")_(") ☃☠ ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
