File Coverage

blib/lib/Math/NumSeq/DedekindPsiSteps.pm

Criterion	Covered	Total	%
statement	67	68	98.5
branch	9	12	75.0
condition	2	3	66.6
subroutine	14	14	100.0
pod	1	1	100.0
total	93	98	94.9

# Copyright 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::DedekindPsiSteps;
use 5.004;
use strict;

use vars '$VERSION', '@ISA';
$VERSION = 71;

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

use Math::NumSeq::PrimeFactorCount;;
*_prime_factors = \&Math::NumSeq::PrimeFactorCount::_prime_factors;

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


# use constant name => Math::NumSeq::__('Dedekind Psi Steps');
use constant description => Math::NumSeq::__('Number of repeated applications of the Dedekind psi function to reach factors 2 and 3 only.');
use constant default_i_start => 1;
use constant characteristic_count => 1;
use constant characteristic_smaller => 1;
use constant characteristic_increasing => 0;
use constant values_min => 0;

# A001615 dedekind psi
# A019268 dedekind psi first requiring n steps
# A019269 number of steps
# A173290 dedekind psi cumulative
#
use constant oeis_anum => 'A019269';

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

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

  my ($good, @primes) = _prime_factors($i);
  return undef unless $good;

  my %primes;
  foreach my $p (@primes) {
    $primes{$p}++;
  }
  my $count = 0;

  my %prime_factors;
  for (;;) {
    delete $primes{'2'};
    delete $primes{'3'};
    last unless %primes;

    ### %primes
    $count++;
    my %next_primes;
    while (my ($p, $e) = each %primes) {
      if (--$e) {
        $next_primes{$p} += $e;
      }
      my $prime_factors_aref = ($prime_factors{$p} ||= do {
        my ($good, @primes) = _prime_factors($p+1);
        return undef unless $good;
        \@primes
      });
      foreach my $f (@$prime_factors_aref) {
        $next_primes{$f}++;
      }
    }
    %primes = %next_primes;
  }
  return $count;
}

# sub _psi_ex23 {
#   my ($n) = @_;
#   ### _psi(): $n
#
#   my $prev = 0;
#   my $ret = 1;
#   foreach my $p (prime_factors($n)) {
#     next if $p == 2 || $p == 3;
#     if ($p == $prev) {
#       $ret *= $p;
#     } else {
#       $ret *= $p+1;
#       $prev = $p;
#     }
#   }
#   return $ret;
#
#   # my %primes;
#   # @primes{prime_factors($n)} = (); # hash slice
#   # delete $primes{2,3}; # hash slice
#   # foreach my $p (keys %primes) {
#   #   $n /= $p;
#   #   $n *= $p+1;
#   # }
#   return $n;
# }

# sub _is_2x3y {
#   my ($n) = @_;
#   until ($n % 2) {
#     $n = int($n/2);
#   }
#   until ($n % 3) {
#     $n = int($n/3);
#   }
#   return ($n == 1);
# }

1;
__END__