# 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::MoranNumbers;
use 5.004;
use strict;
use Math::Prime::XS 0.23 'is_prime'; # version 0.23 fix for 1928099
use vars '$VERSION', '@ISA';
$VERSION = 70;
use Math::NumSeq;
use Math::NumSeq::Base::IteratePred;
@ISA = ('Math::NumSeq::Base::IteratePred',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Devel::Comments;
use constant name => Math::NumSeq::__('Moran Numbers');
use constant description => Math::NumSeq::__('Moran numbers, divisible by the sum of their digits and that division resulting in a prime.');
use constant i_start => 1;
use Math::NumSeq::Base::Digits
'parameter_info_array'; # radix parameter
sub values_min {
my ($self) = @_;
if (! $self->{'values_min'}) {
for (my $value = $self->{'radix'}; ; $value++) {
if ($self->pred($value)) {
$self->{'values_min'} = $value;
last;
}
}
}
return $self->{'values_min'};
}
#------------------------------------------------------------------------------
# cf A007953 digit sum (in Math::NumSeq::DigitSum)
# A085775 both n/digitsum(n) and (n+1)/digitsum(n+1) prime
# A108780 n/digitsum(n) is a golden semiprime
# A130338 primes not occurring as n/digitsum(n)
# A003635 inconsummate, quotients not occuring as n/digitsum(n)
#
my @oeis_anum;
$oeis_anum[10] = 'A001101'; # OFFSET=1
# OEIS-Catalogue: A001101
sub oeis_anum {
my ($self) = @_;
return $oeis_anum[$self->{'radix'}];
}
#------------------------------------------------------------------------------
sub pred {
my ($self, $value) = @_;
### MoranNumbers pred(): $value
if ($value <= 0 || $value != int($value)) {
return 0;
}
if (_is_infinite($value)) {
return undef;
}
my $radix = $self->{'radix'};
my $sum = 0;
my $v = $value;
while ($v) {
$sum += ($v % $radix);
$v = int($v/$radix);
}
if ($value % $sum) {
return 0;
}
$value /= $sum;
if ($value > 0xFFFF_FFFF) {
return undef;
}
return is_prime($value);
}
1;
__END__
=for stopwords Ryde Math-NumSeq moran ie harshad
=head1 NAME
Math::NumSeq::MoranNumbers -- numbers divided by sum of digits giving a prime
=head1 SYNOPSIS
use Math::NumSeq::MoranNumbers;
my $seq = Math::NumSeq::MoranNumbers->new;
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
The Moran numbers,
18, 21, 27, 42, 45, 63, 84, ...
being integers which are divisible by the sum of their digits and that
division resulting in a prime. For example 42 has digit sum 4+2=6 and
42/6=7 is an integer and a prime.
This is a subset of the harshad numbers (L<Math::NumSeq::HarshadNumbers>),
those being all integers divisible by the their digit sum. The further
restriction here is that the division gives a prime.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::MoranNumbers-E<gt>new ()>
=item C<$seq = Math::NumSeq::MoranNumbers-E<gt>new (radix =E<gt> $r)>
Create and return a new sequence object.
The optional C<radix> parameter (default 10, decimal) sets the base to use
for the digits.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> is a Moran number, ie. is divisible by the sum of
its digits in the given C<radix>, and that division gives a prime.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::DigitSum>,
L<Math::NumSeq::HarshadNumbers>
=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