props for using { catalogue and managing a &. application in your step function.
a design principle I was aiming for is a big strength of J. What I call a
"perfect function" defined as iterative form where output is of consistent
shape/meaning as input, and where ^: can be used "separately" to get the
iterations. It means debug free explorative programing. Use adverbs to
integrate extra/domain functionality above the "perfect function"
Your "step" function is actually more pure/more perfect than my ltrunc because
it just returns the raw result of the next iteration.
(1 + i.9) step < 3 7
13 17 23 37 43 47 53 67 73 83 97
to use your step function to get the "exploratory structure" I want/ed just
with adverbs
H =: 2 : 'u v'
> {: (1 + i.9) step H {: ((<@) ,~ ])^:(2) < 3 7
113 137 167 173 197 223 283 313 317 337 347 353 367 373 383 397 443 467 523 547
613 617 643 647 653 673 683 743 773 797 823 853 883 937 947 953 967 983 997
The function and adverbs will still work with data that is truncated to the
last iteration, perhaps if exploration results in memory constraints. Compared
to ^:a: or ^:(i.n), there are no shape/fill cleanups to obtain the count of
each iteration result.
for completeness, a right truncated primes generation function.
original, just edit of my less than fully perfect ltrunc
rtrunc1 =: (] , ((1 3 7 9) (10 #. ,~)"0 1 (10&#.inv))"0(,@:)(selPrime@:)
each@:{:)
Perfect separation of a core perfect function (optimized for wrapped with
adverbs matching my exploration objectives
rtruncCore =: (+ 10 * ])(selPrime@:)"0 1((,@:) -. 0:)
1 3 7 9 rtruncCore 2 3 5 7
31 71 23 53 73 37 29 59 79
rtrunc =: rtruncCore &>/@; H {: ((<@) ,~ ])
> {: 1 3 7 9 rtrunc^:2 < 2 3 5 7
311 313 233 733 373 293 593 317 797 719 239 739 379 599
The &>/@; portion could be part of "core function" and makes it compatible with
either boxed or unboxed y argument. Worth noting that the adverb section is
identical to both "structural applications of the core perfect function".
On Monday, November 21, 2022 at 09:47:27 a.m. EST, Raul Miller
<[email protected]> wrote:
For this, I think I would have gone with:
selPrime=: #~ 1&p:
seed=: selPrime digits=: 1+i.9
step=: selPrime@,@:(,&.(10x&#.inv)/&>)@{@;
digits&step&.>^:a: ,<seed
Which, granted, is not particularly fast. (That last line takes about
15 seconds on my current laptop.)
Not sure if this helps, though...
--
Raul
On Sun, Nov 20, 2022 at 8:37 PM 'Pascal Jasmin' via Programming
<[email protected]> wrote:
>
> based on Raul's rosettacode link, but building an expaning list of left
> truncable primes, such that further search is possible on future "iterations"
>
>
> selPrime=: #~ 1&p:
>
> ltrunc =: (] , ((1+i.9) (10 #. ,)"0 1 (10&#.inv))"0(,@:)(selPrime@:) each@:{:)
>
> # &> sofar =: ltrunc^:6 < 3 7x
>
> 2 11 39 99 192 326 429
>
> # &> sofar =: ltrunc^:6 sofar
>
> 2 11 39 99 192 326 429 521 545 517 448 354 276
>
> the number of truncable primes decreases substantially as the digits
> increase. (last answer is for 1 to 13 digits, with single digit primes
> wrongly listed (4 is right number of single digit primes)
>
> the full list eventually goes to 0
>
> # &> sofar =: ltrunc^:1 sofar (NB. iterations skipped)
>
> 2 11 39 99 192 326 429 521 545 517 448 354 276 212 117 72 42 24 13 6 5 4 3 1 0
>
> which I guess we knew from example number
>
> > _2 { sofar
>
> 357686312646216567629137
>
>
> On Saturday, November 19, 2022 at 07:04:25 p.m. EST, Raul Miller
> <[email protected]> wrote:
>
>
>
>
>
> On Sat, Nov 19, 2022 at 6:47 PM 'Skip Cave' via Programming
> <[email protected]> wrote:
> > Now what is the J verb that will find an n-digit integer that is still
> > prime when each of the digits are removed?
>
> I'd probably go with https://rosettacode.org/wiki/Truncatable_primes#J for
> that.
>
> Thanks,
>
> --
> Raul
>
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