# Copyright 2011, 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
package Math::NumSeq::ReplicateDigits;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Devel::Comments;
# use constant name => Math::NumSeq::__('...');
use constant description => Math::NumSeq::__('Replicate the digits of i, so i=123 gives value 112233.');
use constant default_i_start => 0;
use constant characteristic_integer => 1;
use constant characteristic_increasing => 1;
use Math::NumSeq::DigitCount 4;
use constant parameter_info_array =>
[ Math::NumSeq::Base::Digits::parameter_common_radix(),
{ name => 'replicate',
type => 'integer',
minimum => 1,
default => 2,
width => 1,
},
];
sub values_min {
my ($self) = @_;
return $self->ith($self->i_start);
}
# cf A044836 decimal odd/even runs
#
my @oeis_anum;
$oeis_anum[0]->[10]->[1] = 'A001477';
# OEIS-Other: A001477 replicate=1 # integers 0 upwards
$oeis_anum[1]->[10]->[1] = 'A000027';
# OEIS-Other: A000027 replicate=1 i_start=1 # integers 1 upwards
# no, these repeat whole values, not individual digits
#
# $oeis_anum[1]->[10]->[2] = 'A020338';
# # OEIS-Catalogue: A020338 i_start=1 # doublets 1010,1111,1212
#
# $oeis_anum[1]->[10]->[3] = 'A074842';
# # OEIS-Catalogue: A074842 replicate=3 i_start=1 # triplets
#
# $oeis_anum[1]->[10]->[4] = 'A074843';
# # OEIS-Catalogue: A074843 replicate=4 i_start=1 # quadruplets
sub oeis_anum {
my ($self) = @_;
return $oeis_anum[$self->i_start]->[$self->{'radix'}]->[$self->{'replicate'}];
}
sub ith {
my ($self, $i) = @_;
### ReplicateDigits ith(): $i
if (_is_infinite($i)) {
return $i; # don't loop forever if $i is +infinity
}
my $value = ($i * 0); # inherit bignum 0
my $power = $value + 1; # inherit bignum 1
if ($i < 0) {
$power = -$power;
$i = - $i;
}
my $radix = $self->{'radix'};
my $replicate = $self->{'replicate'};
while ($i) {
my $digit = $i % $radix;
$i = int($i/$radix);
foreach (1 .. $replicate) {
$value += $power * $digit;
$power *= $radix;
}
}
return $value;
}
sub pred {
my ($self, $value) = @_;
my $radix = $self->{'radix'};
my $replicate = $self->{'replicate'};
$value = abs($value);
while ($value) {
my $digit = $value % $radix;
$value = int($value/$radix);
foreach (2 .. $replicate) {
if (($value % $radix) != $digit) {
return 0;
}
$value = int($value/$radix);
}
}
return 1;
}
1;
__END__