File Coverage

blib/lib/Math/NumSeq/HappySteps.pm

Criterion	Covered	Total	%
statement	57	58	98.2
branch	5	6	83.3
condition	1	3	33.3
subroutine	15	15	100.0
pod	3	3	100.0
total	81	85	95.2

# Copyright 2011, 2012, 2013, 2014 Kevin Ryde

# This file is part of Math-NumSeq.
#
# 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 .

package Math::NumSeq::HappySteps;
use 5.004;
use strict;

use vars '$VERSION', '@ISA';
$VERSION = 72;

use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
        'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

# uncomment this to run the ### lines
#use Devel::Comments;


# use constant name => Math::NumSeq::__('Happy Steps');
use constant description => Math::NumSeq::__('How many sum of squares of digits steps to get to a repeating iteration.');
use constant i_start => 1;
use constant values_min => 1;
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_increasing => 0;

use Math::NumSeq::Base::Digits
  'parameter_info_array';   # radix parameter

#------------------------------------------------------------------------------
# cf A001273 smallest happy which takes N steps
#
my @oeis_anum;

$oeis_anum[2] = 'A078627'; # starting i=1 ...
# OEIS-Catalogue: A078627 radix=2

$oeis_anum[10] = 'A193995'; # but starting i=1 ...
# OEIS-Catalogue: A193995

sub oeis_anum {
  my ($self) = @_;
  return $oeis_anum[$self->{'radix'}];
}

#------------------------------------------------------------------------------

sub ith {
  my ($self, $i) = @_;

  if ($i <= 0) {
    return 0;
  }
  if (_is_infinite($i)) {
    return $i;
  }

  my $radix = $self->{'radix'};
  my $steps = 0;
  my %seen;
  for (;;) {
    ### $i
    my $sum = 0;
    if ($seen{$i}) {
      return $steps;
    }
    $seen{$i} = 1;
    while ($i) {
      my $digit = ($i % $radix);
      $sum += $digit * $digit;
      $i = int($i/$radix);
    }
    $i = $sum;
    $steps++;
  }
}

sub pred {
  my ($self, $value) = @_;
  ### HappySteps pred(): $value
  return ($value >= 0 && $value == int($value));
}

1;
__END__