help needed with bases

[Richard Donovan]

Hi

I am doing some work on palindromic primes in any base and I am using

    5 #.^:_1&.> i.100000 

To convert in this case the first 100000 digits to base 5 which I later test to select palindromes.

It gives the right result but takes forever and uses heaps of space:-

ts'10 #.^:_1&.> i.100'

┌─────────┬──────┐

│0.0008306│476224│

└─────────┴──────┘

  ts'10 #.^:_1&.> i.10000'

┌────────┬────────┐

│0.111163│46990272│

└────────┴────────┘

  ts'10 #.^:_1&.> i.100000'

┌────────┬─────────┐

│0.965501│477693888│

└────────┴─────────┘

  ts'5 #.^:_1&.> i.100000'

┌────────┬─────────┐

│0.945648│469305216│

└────────┴─────────┘

Is there anything I can do to improve performance and reduce storage use?

Thanks in advance

Richard Donovan

[Henry Rich]

   (6!:2 , 7!:2)'(#: i.@(*/)) 8$5'
0.0136049 3.35563e7

Not an exact match as it has high-order 0s, but faster.

Henry Rich

To unsubscribe from this group and stop receiving emails from it, send an email to forum+un...@jsoftware.com.

[More Rice]

maybe get rid of the boxes and do palindrome filtering in string?

On my poor machine ...

   timespacex '5 #.^:_1&.> i.100000'  NB. Yours

0.694979 4.69305e8

Here, I tried to do the same + filtering; it still costs less:

   pf =: (#~ (-:|.)"1) NB. guessing this is what you want to do.

   timespacex 'pf ,"2 ":"(0) 5 #.inv i.100000'

0.11806 9.44435e6

Maurice

To unsubscribe from this group and stop receiving emails from it, send an email to forum+un...@jsoftware.com.

[Raul Miller]

It might be that the suggestions you've received are good enough for
your purposes.

That said, I think the purpose of the boxing here is to ignore leading zeros.

So, it might make sense to generate the sequence of numbers
corresponding to some number of digits in the given base.

NB. x base, y digit count
subseq=: {{ x #.inv (x^y-1)+i.x^y-1 }}

Or, better yet, introduce palindrome filtering into the generating function:

palseq=: {{ x #. (#~ ] -:"1 |."1) x #.inv (x^y-1)+i.x^y-1 }}

This generates some extra numbers, but hopefully discarding them
wouldn't be too problematic.

#0,; 5 palseq&.> 1+i.>.5^.1e5
313
#(#~ 1e5>]) 0,; 5 palseq&.> 1+i.>.5^.1e5
223

FYI,

--
Raul

On Mon, Sep 2, 2024 at 10:58 AM Richard Donovan <rsdo...@hotmail.com> wrote:
>
>

[Mike Day]

This constructive approach might be of some use for

producing Richard's pally primes:

ps =: {{

b =. x             NB. base

d =. y             NB. width

hd=. >.-: d                  NB. size of rhs (incl middle if d odd)

i =. b #.inv i. b ^ hd       NB. generate too many rhs,  ie incl 0 in units column

i =. b (]#~(* @ | {:"1)) i   NB. prune out 0s in units col 

10 #. i,. ~ (d-hd){."1|."1 i NB. pin on the lhs, expressed in base 10

}} 

 

eg 

   3 6$3 ps 5

10001 20002 11011 21012 12021 22022

10101 20102 11111 21112 12121 22122

10201 20202 11211 21212 12221 22222

I've returned them as base 10 integers,  but could have kept the result as 

a table of digits,  or indeed a character array.  

Boxing isn't needed, as it ensures that the leading digit is non-zero.

Its performance seems adequate:

   #7 ps 10

14406

   timespacex'7 ps 10'

0.006473 4.19664e6

   

... depending of course on how large the required primes will be!

Mike

Sent from my iPad

On 2 Sep 2024, at 21:28, Raul Miller <rauld...@gmail.com> wrote:

It might be that the suggestions you've received are good enough for

[Michael Day]

Actually it's not much more complicated when avoiding any pruning of
the rhs of the candidate palindromes:

cf my earlier email - below this one -

psa =: {{

b =. x             NB. base
d =. y             NB. width
hd=. >.-: d                                   NB. size of rhs (incl middle if d odd)

bb=. (1,~<: hd) # b - 0 1                     NB. using b-1 in units column
i =. (1 {.~ - hd) +"1 bb #: i. */bb           NB. generate rhs, incrementing units column to avoid zeros
10 #. i,. ~ (d-hd){."1|."1 i NB. pin on the lhs; result is expressed in base 10
}}

    timespacex'5 ps 8'    NB. on my laptop this time

0.000277 67296

    timespacex'5 psa 8'  NB. space much the same!

0.0001156 67424

      (6!:2 , 7!:2)'(#: i.@(*/)) 8$5'    NB. Henry's scoping snapshot on my laptop
0.0186664 3.35563e7

Virus-free.www.avast.com

[More Rice]

(The theme here continued to be boxless.)

more seriously,

   bn =: <.@(1: + (^. >./))

   bdl =: ] #:~ bn # [

   NB. the table of 0-padded digits in base 5; similar to Henry's.

   5 bdl i.100000

   NB. leading zero aware palindrome check and tell you which one. Did I get it right?

   dr =: 1 i."1~ 0&<

   bpldm =: 4 : '(#~ ([: ((-:|.)"1 (|."(0 1)~ dr)) x&bdl)) y'

   NB. looks ok, no?

   4 bpldm 25 0 100 5 514 46 706

25 0 5 514 46

   NB. the finale - number of primes < 100000 that are also palindrome in base 4.

   # 4 bpldm p:i.9591

65

[trx2358...@yahoo.com]

Following Raul’s suggestion to use anti-base to a specified number of digits you could simply remove leading 0’s and let the fill shift them to the end which will line them up when reversed for testing.

   strp=.[ #~ >./\&:*

   ([;|.-:/@,:strp)"1(3#5) #:i.20

┌─────┬─┐

│0 0 0│1│

├─────┼─┤

│0 0 1│1│

├─────┼─┤

│0 0 2│1│

├─────┼─┤

│0 0 3│1│

├─────┼─┤

│0 0 4│1│

├─────┼─┤

│0 1 0│0│

├─────┼─┤

│0 1 1│1│

├─────┼─┤

│0 1 2│0│

├─────┼─┤

│0 1 3│0│

├─────┼─┤

│0 1 4│0│

├─────┼─┤

│0 2 0│0│

├─────┼─┤

│0 2 1│0│

├─────┼─┤

│0 2 2│1│

├─────┼─┤

│0 2 3│0│

├─────┼─┤

│0 2 4│0│

├─────┼─┤

│0 3 0│0│

├─────┼─┤

│0 3 1│0│

├─────┼─┤

│0 3 2│0│

├─────┼─┤

│0 3 3│1│

├─────┼─┤

│0 3 4│0│

└─────┴─┘

P.S. I only subscribe to the digest.  Might it be useful to insert Reply-to links for the individual threads?

Sent from Yahoo Mail for iPhone

On Wednesday, September 4, 2024, 11:39 AM, fo...@jsoftware.com wrote:

help needed with bases 

Mike Day <mike_l...@tiscali.co.uk>: Sep 03 06:10PM +0100

Michael Day <mike_l...@tiscali.co.uk>: Sep 03 07:06PM +0100

Actually it's not much more complicated when avoiding any pruning of the rhs of the candidate palindromes:   cf my earlier email - below this one -   psa =: {{ b =. x             NB. base d =. y             NB. width hd=. >.-: d                                   NB. size of rhs (incl middle if d odd) bb=. (1,~<: hd) # b - 0 1                     NB. using b-1 in units column i =. (1 {.~ - hd) +"1 bb #: i. */bb           NB. generate rhs, incrementing units column to avoid zeros 10 #. i,. ~ (d-hd){."1|."1 i NB. pin on the lhs; result is expressed in base 10 }}       timespacex'5 ps 8'    NB. on my laptop this time   0.000277 67296     timespacex'5 psa 8'  NB. space much the same!   0.0001156 67424             (6!:2 , 7!:2)'(#: i.@(*/)) 8$5'    NB. Henry's scoping snapshot on my laptop 0.0186664 3.35563e7       On 03/09/2024 18:10, 'Mike Day' via forum wrote:

-- This email has been checked for viruses by Avast antivirus software. www.avast.com

Back to top

j9.6.0-beta16 available

bill lam <bbil...@gmail.com>: Sep 04 12:21AM +0800 That should be a bug in J9.6 beta 3 and later. It should be already fixed in beta 17.     On Sat, Aug 10, 2024, 11:28 PM Jan-Pieter Jacobs <janpiete...@gmail.com> wrote:

Jan-Pieter Jacobs <janpiete...@gmail.com>: Sep 03 07:37PM +0200 Thank you Bill, I tried and confirm installing from Github now works.   Jan-Pieter

Back to top

Pairing elements on diagonals

Marcin Żołek <marcin...@students.mimuw.edu.pl>: Sep 03 05:44PM +0200 Thanks! I find your approach (get the indices of elements for each diagonal and then work with flattened array) very useful and universal. I came up with a less universal approach: find pairs of local indices for each diagonal and then map them to the correct indices. Your solution seems more universal to me, because finding pairs is independent of the fact that the task involved diagonals in your case, while in my case it is dependent.   a =: 4 4 $ 1 0 1 1 2 2 1 1 1 2 0 1 2 0 2 2 ((I.@:(=&1) <@:(,/)@:(,."0 1) I.@:(=&2))/. ;@:({&.>) </.@:i.@:$)"2 a 2 5 8 5 3 9 3 12 6 9 6 12 11 14   Marcin

Back to top

You received this digest because you're subscribed to updates for this group. You can change your settings on the group membership page. To unsubscribe from this group and stop receiving emails from it send an email to forum+un...@jsoftware.com.