# Copyright 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::PowerSieve;
use 5.004;
use strict;
use vars '$VERSION','@ISA';
$VERSION = 69;
use Math::NumSeq 7; # v.7 for _is_infinite()
@ISA = ('Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('Lucky Numbers');
use constant description => Math::NumSeq::__('Sieved out multiples according to the sequence itself.');
use constant values_min => 1;
use constant i_start => 1;
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;
use constant parameter_info_array =>
[
{ name => 'base',
share_key => 'base_2',
type => 'integer',
display => Math::NumSeq::__('From Radix'),
default => 2,
minimum => 2,
width => 3,
# description => Math::NumSeq::__('...'),
},
];
#------------------------------------------------------------------------------
# A007951 - ternary sieve, dropping 3rd, 6th, 9th, etc
# 1,2,_,4,5,_,7,8,_,10,11,_,12,13,_,14,15,_
# ^9th
# 1,2,4,5,7,8,10,11,14,16,17,19,20,22,23,25,28,29,31,32,34,35,37,38,41,
my @oeis_anum;
$oeis_anum[3] = 'A007951';
# OEIS-Other: A007951 multiple=3
sub oeis_anum {
my ($self) = @_;
return $oeis_anum[$self->{'base'}];
}
#------------------------------------------------------------------------------
sub rewind {
my ($self) = @_;
$self->{'i'} = $self->i_start;
$self->{'value'} = 0;
my $base = $self->{'base'};
$self->{'count'} = [ $base ];
$self->{'remaining'} = [ $base ];
}
# ENHANCE-ME: Defer pushing each value only the count array until needed.
# Might keep array size down to i/log(i) instead of i.
#
sub next {
my ($self) = @_;
### PowerSieve next(): "i=$self->{'i'}"
### count: $self->{'count'}
### remaining: $self->{'remaining'}
### value: $self->{'value'}
my $count = $self->{'count'};
my $remaining = $self->{'remaining'};
my $value = $self->{'value'};
OUTER: for (;;) {
$value++;
### $value
foreach my $p (0 .. $#$remaining) {
if (--$remaining->[$p] <= 0) {
### exclude at: "p=$p count=$self->{'count'}->[$p]"
$remaining->[$p] = $self->{'count'}->[$p];
next OUTER;
}
}
$self->{'value'} = $value;
my $i = $self->{'i'}++;
if ($i > $count->[-1]) {
my $c = $count->[-1] * $self->{'base'};
push @$count, $c;
push @$remaining, $c - $i;
### extend: "count=$count->[-1] remaining=$remaining->[-1]"
}
return ($i, $value);
}
}
1;
__END__
=for stopwords Ryde Math-NumSeq
=head1 NAME
Math::NumSeq::PowerSieve -- sieved out powers
=head1 SYNOPSIS
use Math::NumSeq::PowerSieve;
my $seq = Math::NumSeq::PowerSieve->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
This is repeated sieving out of powers of a base integer. The default is 2
1, 3, 5, 9, 11, 13, 17, 21, 25, 27, 29, 33, 35, 37, 43, 49, ...
The sieve starts with all integers
1,2,3,4,5,6,7,8,9,10,11,12,13
Then sieve out all the multiple of 2 positions (which leaves the odd
numbers)
1,3,5,7,9,11,13,15,17,19,21,23,25,...
Then sieve out all the multiple of 4 positions, for example 7 at position 4
is the first removed
1,3,5,9,11,13,17,19,21,25,...
Then multiple of 8 positions (value 19 here), then 16, 32, etc.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::PowerSieve-E<gt>new ()>
Create and return a new sequence object.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::ReRound>,
L<Math::NumSeq::ReReplace>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 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