NAME

Math::NumSeq::CollatzSteps -- steps in the "3n+1" problem

SYNOPSIS

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

DESCRIPTION

The number of steps it takes to reach 1 by the Collatz "3n+1" problem,

0, 1, 7, 2, 5, 8, 16, 3, 19, 6, 14, 9, 9, 17, 17, 4, 12, 20, 20, ...
starting i=1

The Collatz problem iterates

n -> / 3n+1  if n odd
     \ n/2   if n even

For example i=6 takes value=8 many steps to reach 1,

6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1

It's conjectured that any starting n will always eventually reduce to 1 and so the number of steps is finite. There's no limit in the code on how many steps counted. Math::BigInt is used if 3n+1 steps go past the usual scalar integer limit.

FUNCTIONS

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

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

$seq = Math::NumSeq::CollatzSteps->new (step_type => $str)

Create and return a new sequence object.

The optional step_type parameter (a string) selects between

"up"      upward steps 3n+1
"down"    downward steps n/2
"both"    both up and down (the default)

Random Access

$value = $seq->ith($i)

Return the number of steps to take $i down to 1.

$bool = $seq->pred($value)

Return true if $value occurs as a step count. This is simply $value >= 0.

SEE ALSO

Math::NumSeq, Math::NumSeq::JugglerSteps, Math::NumSeq::ReverseAddSteps Math::NumSeq::HappySteps

HOME PAGE

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

LICENSE

Copyright 2011, 2012, 2013 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/>.