File Coverage

blib/lib/Math/NumSeq/RepdigitAny.pm

Criterion	Covered	Total	%
statement	80	80	100.0
branch	22	22	100.0
condition	2	3	66.6
subroutine	13	13	100.0
pod	3	3	100.0
total	120	121	99.1

# Copyright 2010, 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::RepdigitAny;
use 5.004;
use strict;

use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq 7; # v.7 for _is_infinite()
@ISA = ('Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

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


# use constant name => Math::NumSeq::__('Repdigit Any Radix');
use constant description => Math::NumSeq::__('Numbers which are a "repdigit" like 1111, 222, 999 etc of 3 or more digits in some number base.');
use constant i_start => 1;
use constant values_min => 0;
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;

# cf A167783 - length >=2, 2 or more bases
#    A053696 - length >=3, 1 or more bases repunit
#
#    A158235 - square is a repdigit in some base < i
#    A158236 - the radix for those squares
#    A158237 - those squares, ie. squares which are repdigits some base
#    A158245 - "primitives" in squares seq, meaning square-free
#
use constant oeis_anum => 'A167782'; # length >=3, 1 or more bases

sub rewind {
  my ($self) = @_;
  $self->{'i'} = $self->i_start;
  $self->{'done'} = 0;
  $self->{'ones'}   = [ undef, undef, 7 ];
  $self->{'digits'} = [ undef, undef, 1 ];
}

sub next {
  my ($self) = @_;
  ### RepdigitAny next(): $self->{'i'}

  my $done;
  if ($done = $self->{'done'}) {
    my $min = $done*$done + 7;
    my $ones = $self->{'ones'};
    my $digits = $self->{'digits'};

    for (my $radix = 2; ; $radix++) {
      ### $radix

      my $one;
      if ($radix > $#$ones) {
        ### maybe extend array: $radix
        $one = ($radix + 1) * $radix + 1;
        if ($one > $min) {
          ### stop at big one: $one
          last;
        }
        $ones->[$radix] = $one;
        $digits->[$radix] = 1;
      } else {
        $one = $ones->[$radix];
      }

      my $repdigit;
      while (($repdigit = $one * $digits->[$radix]) <= $done) {
        ### increase past done: $repdigit
        if (++$digits->[$radix] >= $radix) {
          $digits->[$radix] = 1;
          $one = $ones->[$radix] = $ones->[$radix] * $radix + 1;
          ### digit wrap new ones: $ones->[$radix]
        } else {
          ### digit step: $digits->[$radix]
        }
      }

      ### consider repdigit: $repdigit
      if ($repdigit < $min) {
        ### min now: "$repdigit at $radix"
        $min = $repdigit;
      }
    }
    ### result: $min
    $self->{'done'} = $min;
    return ($self->{'i'}++, $min);

  } else {
    # special case value 0
    $self->{'done'} = 1;
    return ($self->{'i'}++, 0);
  }
}

sub pred {
  my ($self, $value) = @_;
  ### RepdigitAny pred(): $value

  if ($value == 0) {
    return 1;
  }
  if (_is_infinite($value) || $value != int($value)) {
    return 0;
  }

 RADIX: for (my $radix = 2; ; $radix++) {
    my $ones = ($radix + 1) * $radix + 1;
    if ($ones > $value) {
      return 0;
    }

    do {
      if ($ones == $value) {
        return 1;
      }
      foreach my $digit (2 .. $radix-1) {
        my $repdigit = $digit * $ones;
        if ($repdigit == $value) {
          return 1;
        }
        if ($repdigit > $value) {
          next RADIX;
        }
      }
      $ones = $ones * $radix + 1;
    } while ($ones <= $value);
  }
}

1;
__END__