Kaprekar numbers: Difference between revisions

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===Numeric version (medium)===

<lang perl6>sub kaprekar( Int $n, Int :$base = 10 ) {

The addition of <tt>'''race'''</tt>, in two places, allows for concurrent computation, and brings a significant speed-up in running time. <lang perl6>sub kaprekar( Int $n, Int :$base = 10 ) {

my $hi = $n ** 2;

my $lo = 0;

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print " $_" if .&kaprekar for ^10_000;

my $n;

⚫

say "\n\nBase 10 Kaprekar numbers < :10<1_000_000> = ~~", [+] (1 if kaprekar~~ $~~_ for ^1000000)~~;

(^1_000_000).race.map: { $n++ if kaprekar $_ }

⚫

say "\n\nBase 10 Kaprekar numbers < :10<1_000_000> = $n";

say "\nBase 17 Kaprekar numbers < :17<1_000_000>";

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my &k17 = &kaprekar.assuming(:base(17));

my @results;

for ^:17<1000000> -> $n {

(^:17<1_000_000>).race.map: -> $n {

my ($h,$l) = k17 $n;

next unless $l;

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my $s17 = ($n * $n).base(17);

my $h17 = $h.base(17);

~~say~~ "$n $n17 $s17 ($h17 + $s17.substr(* - $h17.chars))";

@results.push: "$n $n17 $s17 ($h17 + $s17.substr(* - max(1,($s17.chars - $h17.chars))))";

}

}</lang>

.say for @results.sort({$^a.chars <=> $^b.chars});</lang>

<pre> 1 9 45 55 99 297 703 999 2223 2728 4879 4950 5050 5292 7272 7777 9999

<pre style="height:35ex">1 9 45 55 99 297 703 999 2223 2728 4879 4950 5050 5292 7272 7777 9999

Base 10 Kaprekar numbers < :10<1_000_000> = 54

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24137568 GGGGGG GGGGGF000001 (GGGGGF + 000001)</pre>

Note that this algorithm allows the null string on the left, taken as zero, which automatically includes 1 as the first element of the sequence.

===Casting out nines (fast)===

<lang perl6>sub kaprekar-generator( :$base = 10 ) {