++ed by:
Kevin Ryde
and 1 contributors

# 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,

``````    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.

# 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 => '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`.

# HOME PAGE

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

# LICENSE

Copyright 2011, 2012 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/>.