# Copyright 2010, 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/>.
package Math::NumSeq::PrimeQuadraticHonaker;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 72;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
use constant name => Math::NumSeq::__('Prime Generating Quadratic of Honaker');
use constant description => Math::NumSeq::__('The quadratic numbers 4*k^2 + 4*k + 59.');
use constant values_min => 59;
use constant characteristic_increasing => 2;
# http://oeis.org/A048988 # only the primes ones
# use constant oeis_anum => undef;
# uncomment this to run the ### lines
#use Smart::Comments;
sub ith {
my ($self, $i) = @_;
return 4*($i + 1)*$i + 59;
}
sub pred {
my ($self, $n) = @_;
return ($n >= 59
&& do {
my $i = sqrt((1/4) * $n - 29/2) -1/2;
($i==int($i))
});
}
1;
__END__