Super-d numbers

Super-d numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A super-d number is a positive integer n such that d × n^d has at least d consecutive digits d where

   2 ≤ d ≤ 9

For instance, 753 is a super-3 number because 3 × 753^3 = 1280873331.

Task

• For d=2 through d=6, show the first 10 super-d numbers.

Extra credit

• Show the first 10 super-7, super-8, and/or super-9 numbers.   (Optional)

See also

• Wolfram MathWorld - Super-d Number
• OEIS: A014569 - Super-3 Numbers

Factor

<lang factor>USING: arrays formatting io kernel lists lists.lazy math math.functions math.ranges math.text.utils prettyprint sequences

IN: rosetta-code.super-d

super-d? ( seq n d -- ? ) tuck ^ * 1 digit-groups subseq? ;

super-d ( d -- list )

   [ dup <array> ] [ drop 1 lfrom ] [ ] tri [ super-d? ] curry
   with lfilter ;

super-d-demo ( -- )

   10 2 6 [a,b] [
       dup "First 10 super-%d numbers:\n" printf
       super-d ltake list>array [ pprint bl ] each nl nl
   ] with each ;

MAIN: super-d-demo</lang>

Output:

First 10 super-2 numbers:
19 31 69 81 105 106 107 119 127 131 

First 10 super-3 numbers:
261 462 471 481 558 753 1036 1046 1471 1645 

First 10 super-4 numbers:
1168 4972 7423 7752 8431 10267 11317 11487 11549 11680 

First 10 super-5 numbers:
4602 5517 7539 12955 14555 20137 20379 26629 32767 35689 

First 10 super-6 numbers:
27257 272570 302693 323576 364509 502785 513675 537771 676657 678146 

Perl 6

via map + grep:k + .index

Works with: Rakudo version 2019.07.1

2 - 6 takes a few seconds, 7 & 8 take a few minutes; I got tired of waiting for 9.

<lang perl6>my \n = 10;

sub super ($d) {

   my $run = $d x $d;
   "First {n} super-{$d} numbers:\n{ (^Inf .map( 0 ~ $d * * ** $d ).grep: *.index($run), :k)[^n] }\n"

}

1. Required

.say for (2..6).map: -> $d { super $d }

1. Optional

.say for (7..8).map: -> $d { super $d }</lang>

First 10 super-2 numbers:
19 31 69 81 105 106 107 119 127 131

First 10 super-3 numbers:
261 462 471 481 558 753 1036 1046 1471 1645

First 10 super-4 numbers:
1168 4972 7423 7752 8431 10267 11317 11487 11549 11680

First 10 super-5 numbers:
4602 5517 7539 12955 14555 20137 20379 26629 32767 35689

First 10 super-6 numbers:
27257 272570 302693 323576 364509 502785 513675 537771 676657 678146

First 10 super-7 numbers:
140997 490996 1184321 1259609 1409970 1783166 1886654 1977538 2457756 2714763

First 10 super-8 numbers:
185423 641519 1551728 1854230 6415190 12043464 12147605 15517280 16561735 18542300

via grep + .contains in lazy array

<lang perl6> for 2..6 -> $d {

   my $digits = $d x $d;
   
   my @super = grep { ($_ ** $d  *  $d).contains($digits) }, ^Inf;

   say "$d: ", @super.head(10);

} </lang>

Output:

2: (19 31 69 81 105 106 107 119 127 131)
3: (261 462 471 481 558 753 1036 1046 1471 1645)
4: (1168 4972 7423 7752 8431 10267 11317 11487 11549 11680)
5: (4602 5517 7539 12955 14555 20137 20379 26629 32767 35689)
6: (27257 272570 302693 323576 364509 502785 513675 537771 676657 678146)