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


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


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

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

It's conjectured that any starting n will always eventually reduce to 1, 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.


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

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

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, which is 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.


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



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 <>.