# 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::FibonacciProducts;
use 5.004;
use strict;
use vars '$VERSION', '@ISA';
$VERSION = 72;
use Math::NumSeq;
use Math::NumSeq::Base::IteratePred;
@ISA = ('Math::NumSeq',
'Math::NumSeq::Base::IteratePred');
*_is_infinite = \&Math::NumSeq::_is_infinite;
use Math::NumSeq::Fibonacci;
# uncomment this to run the ### lines
#use Smart::Comments;
use constant name => Math::NumSeq::__('Fibonacci Products');
use constant description => Math::NumSeq::__('Numbers which can be formed by multiplying together some set of Fibonacci numbers.');
use constant default_i_start => 1;
use constant values_min => 1;
#------------------------------------------------------------------------------
# cf A065105 not products values_type=>'non_products'
# A049997 fib product of two
# A094563 fib product of three
# A178772 fib integers, muls and divs
# A049996 diffs
# A049998 diffs
# A049999 diff index
# A065885 triplets of consecutive k,k+1,k+2 all Fibonacci products
#
# use constant oeis_anum => 'A065108';
#------------------------------------------------------------------------------
sub pred {
my ($self, $value) = @_;
### FibonacciProducts pred(): "$value"
if (_is_infinite($value)) {
return undef;
}
if ($value != int($value) || $value < 1) {
return 0;
}
if ($value == 1) {
return 1;
}
my (@value,@i);
my $limit = $value;
my $fib = Math::NumSeq::Fibonacci->new;
$fib->seek_to_i(3); # starting from F[3]=2
my ($i, $f);
for (;;) {
($i, $f) = $fib->next;
### $i
### $f
### assert: $f >= 2
if ($f <= $value) {
while (($value % $f) == 0) {
push @value, $value;
push @i, $i;
### divide out ...
$value /= $f;
if ($value == 1) {
### found ...
return 1;
}
}
} else {
### backtrack ...
if (@value) {
$value = pop @value;
$i = pop @i;
$fib->seek_to_i($i+1);
} else {
### no combination found ...
return 0;
}
}
}
}
1;
__END__