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.
step_typeparameter (a string) selects between
"up" upward steps 3n+1 "down" downward steps n/2 "both" both up and down, which is the default
$value = $seq->ith($i)
Return the number of steps to take
$idown to 1.
$bool = $seq->pred($value)
Return true if
$valueoccurs as a step count. This is simply
$value >= 0.
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.
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