# 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/>.
# math-image --values=BaumSweet --path=ZOrderCurve
#
# radix parameter ?
package Math::NumSeq::BaumSweet;
use 5.004;
use strict;
use vars '$VERSION','@ISA';
$VERSION = 72;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('Baum-Sweet');
use constant description => Math::NumSeq::__('Baum-Sweet sequence, 1 if i contains no odd-length run of 0-bits, 0 if it does.');
use constant default_i_start => 0;
use constant values_min => 0;
use constant values_max => 1;
use constant characteristic_integer => 1;
# cf A037011 "Baum Sweet cubic"
# a(k)=1 iff k/3 is in A003714 fibbinary
#
use constant oeis_anum => 'A086747'; # starting OFFSET=0 value 1
sub ith {
my ($self, $i) = @_;
### BaumSweet ith(): $i
if (_is_infinite($i)) {
return $i;
}
while ($i >= 1) {
if (($i % 2) == 0) {
my $oddzeros = 0;
do {
$oddzeros ^= 1;
$i /= 2;
} until ($i % 2);
if ($oddzeros) {
return 0;
}
}
$i = int($i/2);
}
return 1;
}
sub pred {
my ($self, $value) = @_;
return ($value == 0 || $value == 1);
}
1;
__END__
=for stopwords Ryde Math-NumSeq BaumSweet ie
=head1 NAME
Math::NumSeq::BaumSweet -- Baum-Sweet sequence
=head1 SYNOPSIS
use Math::NumSeq::BaumSweet;
my $seq = Math::NumSeq::BaumSweet->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
The Baum-Sweet sequence
1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, ...
starting i=0
where each value is 1 if the index i contains no odd-length run of 0-bits,
or 0 if it does.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::BaumSweet-E<gt>new ()>
Create and return a new sequence object.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return the C<$i>'th BaumSweet number, ie. 1 or 0 according to whether C<$i>
is without or with an odd-length run of 0-bits.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> occurs in the sequence, which simply means 0 or 1.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::GolayRudinShapiro>,
L<Math::NumSeq::Fibbinary>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 2011, 2012, 2013, 2014 Kevin Ryde
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/>.
=cut