(<. + 0 2 {~ 0 0.5 i. 1&|) 1 1.5 2 2.5
1 3 2 4
(+ 3 * (-<.)) 1 1.5 2 2.5
1 3 2 4
(+ 3 * 1&|) 1 1.5 2 2.5
1 3 2 4
I think you meant '1.5+S' instead of '2+S'
Henry Rich
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On Behalf Of Dan Bron
> Sent: Thursday, July 31, 2008 2:04 PM
> To: Programming forum
> Subject: [Jprogramming] Hofstadter-Conway $10,000 Sequence
>
> I'm looking for a cutesy way to express the following:
>
> (<. + 0 2 {~ 0 0.5 i. 1&|)
>
> The input is a vector of non-negative real numbers, which are
> either integers or whose fractional part is one-half.
> Equivalently, the input is -: V where V is a vector of
> non-negative integers.
>
> The output is a vector of non-negative integers, similar to
> the input, but where each non-integer scalar S has been
> replaced with 2+S (the integer scalars have been left alone).
>
>
> -Dan
>
>
> PS: The application is in the context of the iterated
> batrachion function (hcs n) - n%2 where hcs is the
> "Hofstadter-Conway $10,000 Sequence". See the right graphic
> in the first figure at
>
>
> http://mathworld.wolfram.com/Hofstadter-Conway10000-DollarSequ
> ence.html
>
> You can plot it in J with:
>
> require 'plot'
>
> hcs =: 1:`((] +&:$: -) $:@:<:)@.(2&<) M.
> NB. Hofstadter-Conway $10,000 Sequence
> batrachion =: hcs - -:
>
> plot batrachion"0 i. 1000
>
> While investigating this function, I noticed that hcs was
> in the OEIS (it's A004001 [1]), but (hcs n) - n%2 is not.
> I decided to add it (and evangelize J a bit, because I think
> the verb hcs shows J off well), but then I realized why it
> wasn't in there in the first place: it contains non-integers.
>
> So I need to convert the non-integers to integers. The first
> thing that popped into my head was to take the sum of the
> denominators of the egyptian fraction expansion of each
> scalar. Adapting Roger's ef verb [2] a bit, I came up with:
>
>
> ef =: ( ((] , $:@:(- %)) >:)^:((~: %)~)
> <.@:% ) M. NB. Egyptian fraction denominators
> ib =: +/@:ef@:batrachion"0
> NB. Integer batrachion
>
> plot _&=`(,:&0)} ib i. 1000
>
> But then I realized this was overkill, because each scalar is
> either an integer (and N = +/@:ef N is a tautology for
> integer N ), or halfway between two integers, which means
> all the denominators but the last are 1 , and the last is
> always 2 .
>
> So now we have:
>
> lef =: (<. + 0 2 {~ 0 0.5 i. 1&|)
> NB. "Limited" egyptian fraction
> ib2 =: +/@:lef@:batrachion"0
>
> plot ib2"0 i. 1000
>
> But I would really like to show off J, and I feel that lef
> is just too "brute force" (imperative). Further, OEIS has a
> very mathematical emphasis, and les has a programming bent.
> So I would really like a cuter, more mathematical replacement.
>
> If you provide one, the bonus is you get your name
> immortalized in the OEIS (as a reference and a link to your message).
>
> [1] http://www.research.att.com/~njas/sequences/A004001
> [2]
> http://www.jsoftware.com/pipermail/programming/2005-November/0
> 00064.html
>
> ----------------------------------------------------------------------
> For information about J forums see
> http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
