# Copyright 2012 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 .
# Should values in cycles be all 0 ?
package Math::NumSeq::AlphabeticalLengthSteps;
use 5.004;
use strict;
use List::Util 'min';
use vars '$VERSION', '@ISA';
$VERSION = 2;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
use Math::NumSeq::AlphabeticalLength;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('...');
use constant description => Math::NumSeq::__('Steps of alphabetical length until reaching a cycle.');
use constant default_i_start => 1;
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_integer => 1;
*parameter_info_array
= \&Math::NumSeq::AlphabeticalLength::parameter_info_array;
sub values_min {
my ($self) = @_;
### oeis_anum: $self
if (defined (my $values_min = $self->{'values_min'})) {
return $values_min;
}
my $i_start = $self->i_start;
return ($self->{'values_min'}
= min (map {$self->ith($_)}
$i_start .. $i_start + 20));
}
#------------------------------------------------------------------------------
# A133418 single step towards 4
my %oeis_anum = (A005589 => 'A016037', # en cardinals
);
sub oeis_anum {
my ($self) = @_;
return $oeis_anum{$self->{'lenseq'}->oeis_anum || ''};
}
# forty two = 8
# eight = 5
# five = 4
# four = 4
# forty three = 10
# ten = 3
# three = 5
# five = 4
# four = 4
#
# forty three = 11 ... is 5 steps
# forty four = 9
# nine = 4
# four = 4
# fifty seven = 11
# eleven = 6
# size = 3
# three = 5
# five = 4
# four = 4 is 5 steps
#
# fifty seven = 10 ... is 4 steps
#------------------------------------------------------------------------------
sub new {
### AlphabeticalLengthSteps new(): @_
my $self = shift->SUPER::new(@_);
$self->{'lenseq'} = Math::NumSeq::AlphabeticalLength->new(@_);
return $self;
}
sub ith {
my ($self, $i) = @_;
### AlphabeticalLengthSteps ith(): $i
if (_is_infinite($i)) {
return undef;
}
my $count = 0;
my %seen;
for (;;) {
$seen{$i} = undef;
$i = $self->{'lenseq'}->ith($i);
if (! defined $i) {
return undef;
}
### to: $i
last if exists $seen{$i};
$count++;
}
return $count;
}
1;
__END__
# =head2 Lang
#
# The default is English, or the C option can select anything known to
# L. For example French,
#
# lang => 'fr'
# 5, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, ...
#
# The first cycle is at i=3="trois" has 5 letters, 5="cinq" has 4 letters,
# 4="quatre" has 6 letters, 6="six" has 3 letters.
=for stopwords Ryde Math-NumSeq
=head1 NAME
Math::NumSeq::AlphabeticalLengthSteps -- iterations of length in characters
=head1 SYNOPSIS
use Math::NumSeq::AlphabeticalLengthSteps;
my $seq = Math::NumSeq::AlphabeticalLengthSteps->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
This is a count of how many times iterating
S* AlphabeticalLength(i)> until reaching a cycle.
i = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
value = 3, 3, 2, 0, 1, 3, 2, 2, 1, 3, 4, 4, 3, 3, 3, ...
For example i=6="six" is 3 letters, then 3="three" is 5 letters, 5="five" is
4 letters, and 4="four" is its own length. This took 3 steps to reach the
cycle at 4-E4. At i=4 the value is 0 for no steps to reach a cycle
"four"=4.
=head1 FUNCTIONS
See L for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::AlphabeticalLengthSteps-Enew ()>
=item C<$seq = Math::NumSeq::AlphabeticalLengthSteps-Enew (lang =E $str)>
Create and return a new sequence object.
=back
=head2 Random Access
=over
=item C<$value = $seq-Eith($i)>
Return the number times to apply AlphabeticalLength until reaching a cycle.
=cut
=back
=head1 SEE ALSO
L,
L
=head1 HOME PAGE
http://user42.tuxfamily.org/math-numseq/index.html
=head1 LICENSE
Copyright 2012 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 .
=cut
*