Minimum positive multiple in base 10 using only 0 and 1
say $_ , ': ', (1..*).map( *.base(2) ).first: * %% $_ for flat 1..10, 95..105; # etc.sub Ed-Pegg-jr (\n) {
return 1 if n == 1;
my ($count, $power-mod-n) = 0, 1;
my @oom-mod-n = 0; # orders of magnitude of 10 mod n
my @dig-mod = 0; # 1 to n + oom mod n
for 1..n -> \i {
@oom-mod-n[i] = $power-mod-n;
for 1..n -> \j {
my \k = (j + $power-mod-n - 1) % n + 1;
@dig-mod[k] = i if @dig-mod[j] and @dig-mod[j] != i and !@dig-mod[k];
}
@dig-mod[$power-mod-n + 1] ||= i;
($power-mod-n *= 10) %= n;
last if @dig-mod[1];
}
my ($b10, $remainder) = '', n;
while $remainder {
my $place = @dig-mod[$remainder % n + 1];
$b10 ~= '0' x ($count - $place) if $count > $place;
$count = $place - 1;
$b10 ~= '1';
$remainder = (n + $remainder - @oom-mod-n[$place]) % n;
}
$b10 ~ '0' x $count
}
printf "%5s: %28s %s\n", 'Number', 'B10', 'Multiplier';
for flat 1..10, 95..105, 297, 576, 594, 891, 909, 999, 1998, 2079, 2251, 2277, 2439, 2997, 4878 {
printf "%6d: %28s %s\n", $_, my $a = Ed-Pegg-jr($_), $a / $_;
}Output:
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