NAME

Math::NumSeq::LucasSequenceModulo -- number of applications of the PisanoPeriod until a fixed value

SYNOPSIS

use Math::NumSeq::LucasSequenceModulo;
my $seq = Math::NumSeq::LucasSequenceModulo->new;
my ($i, $value) = $seq->next;

DESCRIPTION

This is the number of times the PisanoPeriod must be applied before reaching an unchanging value.

0, 4, 3, 2, 3, 1, 2, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 2, ...
starting i=1

Per Fulton and Morris, repeatedly applying the PisanoPeriod eventually reaches a value m which has PisanoPeriod(m)==m. For example i=5 goes

PisanoPeriod(5)=20
PisanoPeriod(20)=60
PisanoPeriod(60)=60
PisanoPeriod(120)=120
so value=3 applications until to reach unchanging 120

FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::LucasSequenceModulo->new ()

Create and return a new sequence object.

SEE ALSO

Math::NumSeq, Math::NumSeq::Fibonacci

HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE

Copyright 2012, 2013, 2014, 2016, 2019, 2020 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/>.