# Copyright 2012, 2015 Kevin Ryde
# This file is part of Math-NumSeq-Alpha.
#
# Math-NumSeq-Alpha 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-Alpha 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-Alpha. If not, see <http://www.gnu.org/licenses/>.
# cf A000787 - strobogramatic rotate 180
# A007284 - symmetric flipped across horizontal line, digits 0,1,3,8 only
package Math::NumSeq::SevenSegments;
use 5.004;
use strict;
use List::Util 'min','max','sum';
use vars '$VERSION', '@ISA';
$VERSION = 3;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
use Math::NumSeq::Repdigits;
*_digit_split_lowtohigh = \&Math::NumSeq::Repdigits::_digit_split_lowtohigh;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('...');
use constant description => Math::NumSeq::__('Number of segments for i written in 7-segment calculator display.');
use constant default_i_start => 0;
use constant values_min => 2; # "1" using 2 segments
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_integer => 1;
use constant parameter_info_array =>
[
{
name => 'seven',
display => ('Seven'),
type => 'integer',
default => 3,
minimum => 3,
maximum => 4,
description => ('How many segments to count for "7".'),
},
{
name => 'nine',
display => ('Nine'),
type => 'integer',
default => 5,
minimum => 5,
maximum => 6,
description => ('How many segments to count for "9".'),
},
];
#------------------------------------------------------------------------------
# 7 choice of --- ---
# | | |
#
# | |
#
# 9 choice of --- ---
# | | | |
# --- ---
# | |
# ---
#
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
# A063720 6, 2, 5, 5, 4, 5, 5, 3, 7, 5, 8, 4, 7, 7, 6, 7, 7, 5, 9, 7, 11, 7, 10
# A006942 6, 2, 5, 5, 4, 5, 6, 3, 7, 6, 8, 4, 7, 7, 6, 7, 8, 5, 9, 8, 11, 7, 10
# A074458 6, 2, 5, 5, 4, 5, 6, 4, 7, 5
# A010371 6, 2, 5, 5, 4, 5, 6, 4, 7, 6, 8, 4, 7, 7, 6, 7, 8, 6, 9, 8, 11, 7, 10
# A000787 Strobogrammatic
# A018846 Strobogrammatic same upside down
# A018848 same upside down squares, not seven seg
# A018847 same upside down primes
# A018849 same upside down squares, seven-seg
# A053701 vertically symmetric
# A007284 - horizontally symmetric
# A074459 num segments changed to display n+1
#
# A027389 count endpoints of digits, so 0 has none, 6 has one, others have 2
my %oeis_anum = ('5,3,5' => 'A063720',
'6,3,6' => 'A006942',
'6,4,5' => 'A074458',
'6,4,6' => 'A010371',
);
sub oeis_anum {
my ($self) = @_;
my $digit_segments = $self->{'digit_segments'};
return $oeis_anum{join(',',@{$digit_segments}{'6','7','9'})}; # hash slice
}
#------------------------------------------------------------------------------
sub new {
my $self = shift->SUPER::new(@_);
### $self
$self->{'digit_segments'} = { 0 => 6,
1 => 2,
2 => 5,
3 => 5,
4 => 4,
5 => 5,
6 => ($self->{'six'} || 6),
7 => $self->{'seven'},
8 => 7,
9 => $self->{'nine'},
'-' => 1, # secret support for negatives
};
return $self;
}
sub ith {
my ($self, $i) = @_;
### SevenSegments ith(): "$i"
if (_is_infinite($i)) {
return undef;
}
my $digit_segments = $self->{'digit_segments'};
return sum (0, map {$digit_segments->{$_}||0} split(//,$i));
}
1;
__END__
=for stopwords Ryde Math-NumSeq
=head1 NAME
Math::NumSeq::SevenSegments -- count of segments to display by 7-segment LED
=head1 SYNOPSIS
use Math::NumSeq::SevenSegments;
my $seq = Math::NumSeq::SevenSegments->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
This is how many segments are lit to display i in 7-segment LEDs
i = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
value = 6, 2, 5, 5, 4, 5, 6, 3, 7, 5, 8, 4, 7, 7, 6, 7, 8 ...
The segments for each digit are
--- --- ---
| | | | | | |
--- --- ---
| | | | | |
--- --- ---
--- --- --- --- ---
| | | | | | |
--- --- --- ---
| | | | | | |
--- --- ---
Options C<seven =E<gt> $integer> and C<nine =E<gt> $integer> options give
how many segments those digits should be reckoned. Sometimes 7 and 9 have
"serif" segments like the following. C<seven =E<gt> 4> and C<nine =E<gt> 6>
gives this style
--- ---
| | | |
---
| |
---
Total segments for i is similar to L<Math::NumSeq::DigitSum>, but with
digits mapped through a table of segment counts 0-E<gt>6, 1-E<gt>2,
2-E<gt>5, etc.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::SevenSegments-E<gt>new ()>
=item C<$seq = Math::NumSeq::SevenSegments-E<gt>new (seven =E<gt> $int, nine =E<gt> $int)>
Create and return a new sequence object.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return the number of segments to display C<$i> in 7-segment LEDs.
=item C<$i = $seq-E<gt>i_start ()>
Return 0, the first term in the sequence being at i=0.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::DigitSum>,
L<Math::NumSeq::DigitLength>,
L<Math::NumSeq::AlphabeticalLength>
L<Tk::SevenSegmentDisplay>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 2012, 2015 Kevin Ryde
Math-NumSeq-Alpha 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-Alpha 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-Alpha. If not, see L<http://www.gnu.org/licenses/>.
=cut