Eban numbers: Difference between revisions

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===Algorithmically generate / count===

Alternately, a translation of Perl 6~~. Allows for variable and multi character 'bans'~~. Does not need to actually generate the *-ban numbers to count them. Display counts up to 10**21.

Alternately, a partial translation of Perl 6. Does not need to actually generate the e-ban numbers to count them. Display counts up to 10**21.

<lang perl>use strict;

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}

for my $t ('e~~', 't', 'subur~~') {

for my $t ('e') {

my @bans = enumerate($t, 4);

my @count = count($t, my $max = 21);

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Up to and including ten quintillion: 255,999,999

Up to and including one hundred quintillion: 1,279,999,999

Up to and including one sextillion: 1,279,999,999

Up to and including one sextillion: 1,279,999,999</pre>

============= t-ban: =============

t-ban numbers up to 1000: 56

[0 1 4 5 6 7 9 11 100 101 104 105 106 107 109 111 400 401 404 405 406 407 409 411 500 501 504 505 506 507 509 511 600 601 604 605 606 607 609 611 700 701 704 705 706 707 709 711 900 901 904 905 906 907 909 911]

t-ban numbers between 1,000 & 4,000 (inclusive): 0

[]

Counts of t-ban numbers up to one sextillion

Up to and including ten: 7

Up to and including one hundred: 9

Up to and including one thousand: 56

Up to and including ten thousand: 56

Up to and including one hundred thousand: 56

Up to and including one million: 57

Up to and including ten million: 392

Up to and including one hundred million: 393

Up to and including one billion: 2,745

Up to and including ten billion: 19,208

Up to and including one hundred billion: 19,209

Up to and including one trillion: 134,456

Up to and including ten trillion: 134,456

Up to and including one hundred trillion: 134,456

Up to and including one quadrillion: 134,457

Up to and including ten quadrillion: 941,192

Up to and including one hundred quadrillion: 941,193

Up to and including one quintillion: 6,588,344

Up to and including ten quintillion: 6,588,344

Up to and including one hundred quintillion: 6,588,344

Up to and including one sextillion: 6,588,344

============= subur-ban: =============

subur-ban numbers up to 1000: 35

[1 2 5 8 9 10 11 12 15 18 19 20 21 22 25 28 29 50 51 52 55 58 59 80 81 82 85 88 89 90 91 92 95 98 99]

subur-ban numbers between 1,000 & 4,000 (inclusive): 0

[]

Counts of subur-ban numbers up to one sextillion

Up to and including ten: 6

Up to and including one hundred: 35

Up to and including one thousand: 35

Up to and including ten thousand: 35

Up to and including one hundred thousand: 35

Up to and including one million: 36

Up to and including ten million: 216

Up to and including one hundred million: 1,295

Up to and including one billion: 1,295

Up to and including ten billion: 1,295

Up to and including one hundred billion: 1,295

Up to and including one trillion: 1,295

Up to and including ten trillion: 1,295

Up to and including one hundred trillion: 1,295

Up to and including one quadrillion: 1,295

Up to and including ten quadrillion: 1,295

Up to and including one hundred quadrillion: 1,295

Up to and including one quintillion: 1,295

Up to and including ten quintillion: 1,295

Up to and including one hundred quintillion: 1,295

Up to and including one sextillion: 1,295</pre>

=={{header|Perl 6}}==

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sub enumerate ($n, $upto) {

my @ban = nban(1 .. 99, $n);

my @ban = [nban(1 .. 99, $n)],;

my @orders ~~= (2 .. $upto).map({ 10**$_ X* 1..9 }).map: *.&nban($n)~~;

my @orders;

~~@orders~~.map: {

(2 .. $upto).map: -> $o {

given $o % 3 { # Compensate for irregulars: 11 - 19

next unless +$_;

when 0 { @orders.push: [[flat (10**$o X* 1..9).map: *.&nban($n)],

[flat (10**$o X* 11..19).map: *.&nban($n)]]}

when 1 { @orders.push: [flat (10**$o X* 2..9).map: *.&nban($n)] }

default { @orders.push: [flat (10**$o X* 1..9).map: *.&nban($n)] }

}

my @those;

^@orders .map: -> $o {

@ban.push: [] and next unless +@orders[$o];

my @these;

~~.map: {~~ @~~these.append:~~ ~~flat $_, flat~~ @~~ban X+~~ $~~_ }~~;

my @lower = |@orders[$o];

~~@ban.append:~~ @~~these~~

my @upper = [];

if @orders[$o][0].^name eq 'Array' {

@lower = |@orders[$o][0];

@upper = |@orders[$o][1];

}

@lower.map: -> $m {

@these.push: $m;

for ^@ban -> $b {

next unless +@ban[$b];

@these.push: $_ for (flat @ban[$b]) »+» $m ;

}

@ban.push: @those.clone if +@those;

@those = ();

@upper.map: -> $m {

@those.push: $m;

for ^(@ban) -> $b {

next unless +@ban[$b];

@those.push: $_ for (flat @ban[$b]) »+» $m ;

}

@ban.push: @these;

}

@ban.push: @those.clone if +@those;

@ban.unshift(0) if nban(0, $n);

@ban

flat @ban.map: *.flat;

}

sub count ($n, $upto) {

my @orders ~~= (2 .. $upto).map({ 10**$_ X* 1..9 }).map: *.&nban($n)~~;

my @orders;

(2 .. $upto).map: -> $o {

given $o % 3 { # Compensate for irregulars: 11 - 19

when 0 { @orders.push: [[flat (10**$o X* 1 .. 9).map: *.&nban($n)],

[flat (10**$o X* 11..19).map: *.&nban($n)]]}

when 1 { @orders.push: [flat (10**$o X* 2 .. 9).map: *.&nban($n)] }

default { @orders.push: [flat (10**$o X* 1 .. 9).map: *.&nban($n)] }

}

my @count = +nban(1 .. 99, $n);

my $those;

@count.push: @count.sum * @orders[$_] + @orders[$_] for ^(+@orders - 1);

^@orders .map: -> $o {

@count.push: 0 and next unless +@orders[$o];

my @lower = |@orders[$o];

my @upper = [];

if @orders[$o][0].^name eq 'Array' {

@lower = |@orders[$o][0];

@upper = |@orders[$o][1];

}

my $prev = so (@lower.first( { $_ ~~ /^ '1' '0'+ $/ } ) // 0 );

my $sum = @count.sum;

my $these = +@lower * $sum + @lower;

@count[1 + $o] += $those if $those;

$those = +@upper * $sum + @upper;

$these-- if $prev;

@count[1 + $o] += $these;

++@count[$o] if $prev;

}

@count[*-1] += $those if $those and $upto % 3 == 1;

++@count[0] if nban(0, $n);

for ^(@count - 1) { if @orders[$_].contains(1) { @count[$_]++; @count[$_ + 1]-- } }

[\+] @count;

}

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"\nCounts of {$n}-ban numbers up to {cardinal 10**$upto}"

;

my $s = max (1..$upto).map: { (10**$_).&cardinal.chars };

@counts.unshift: @bans.first: * > 10, :k;

for ~~@counts.kv~~ -> ~~$k,~~ $c {

for ^$upto -> $c {

printf "Up to and including %{$s}s: %s\n", cardinal(10**($k+1)), comma($c);

printf "Up to and including %{$s}s: %s\n", cardinal(10**($c+1)), comma(@counts[$c]);

}

}</lang>

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Up to and including ten million: 392

Up to and including one hundred million: 393

Up to and including one billion: 2,~~745~~

Up to and including one billion: 2,801

Up to and including ten billion: 19,~~208~~

Up to and including ten billion: 19,600

Up to and including one hundred billion: 19,~~209~~

Up to and including one hundred billion: 19,601

Up to and including one trillion: ~~134~~,~~456~~

Up to and including one trillion: 140,000

Up to and including ten trillion: ~~134~~,~~456~~

Up to and including ten trillion: 140,000

Up to and including one hundred trillion: ~~134~~,~~456~~

Up to and including one hundred trillion: 140,000

Up to and including one quadrillion: ~~134~~,~~457~~

Up to and including one quadrillion: 140,001

Up to and including ten quadrillion: ~~941~~,~~192~~

Up to and including ten quadrillion: 980,000

Up to and including one hundred quadrillion: ~~941~~,~~193~~

Up to and including one hundred quadrillion: 980,001

Up to and including one quintillion: 6,~~588~~,~~344~~

Up to and including one quintillion: 7,000,000

Up to and including ten quintillion: 6,~~588~~,~~344~~

Up to and including ten quintillion: 7,000,000

Up to and including one hundred quintillion: 6,~~588~~,~~344~~

Up to and including one hundred quintillion: 7,000,000

Up to and including one sextillion: 6,~~588~~,~~344~~

Up to and including one sextillion: 7,000,000

============= subur-ban: =============

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Up to and including one hundred thousand: 35

Up to and including one million: 36

Up to and including ten million: ~~216~~

Up to and including ten million: 215

Up to and including one hundred million: 1,~~295~~

Up to and including one hundred million: 1,259

Up to and including one billion: 1,~~295~~

Up to and including one billion: 1,259

Up to and including ten billion: 1,~~295~~

Up to and including ten billion: 1,259

Up to and including one hundred billion: 1,~~295~~

Up to and including one hundred billion: 1,259

Up to and including one trillion: 1,~~295~~

Up to and including one trillion: 1,259

Up to and including ten trillion: 1,~~295~~

Up to and including ten trillion: 1,259

Up to and including one hundred trillion: 1,~~295~~

Up to and including one hundred trillion: 1,259

Up to and including one quadrillion: 1,~~295~~

Up to and including one quadrillion: 1,259

Up to and including ten quadrillion: 1,~~295~~

Up to and including ten quadrillion: 1,259

Up to and including one hundred quadrillion: 1,~~295~~

Up to and including one hundred quadrillion: 1,259

Up to and including one quintillion: 1,~~295~~

Up to and including one quintillion: 1,259

Up to and including ten quintillion: 1,~~295~~

Up to and including ten quintillion: 1,259

Up to and including one hundred quintillion: 1,~~295~~

Up to and including one hundred quintillion: 1,259

Up to and including one sextillion: 1,~~295~~</pre>

Up to and including one sextillion: 1,259</pre>

Note that the limit to one sextillion is somewhat arbitrary and is just to match the task parameters.

This will quite happily count *-bans up to one hundred centillion. (10<sup>305</sup>) It takes longer, but still ~~less~~ ~~than~~ 10 seconds.

This will quite happily count *-bans up to one hundred centillion. (10<sup>305</sup>) It takes longer, but still on the order of seconds, not minutes.

<pre>Counts of e-ban numbers up to one hundred centillion

...