1Math::NumSeq::DigitProdUuscetrStCeopnst(r3i)buted Perl DMoactuhm:e:nNtuamtSieoqn::DigitProductSteps(3)
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NAME

6       Math::NumSeq::DigitProductSteps -- multiplicative persistence and
7       digital root
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SYNOPSIS

10        use Math::NumSeq::DigitProductSteps;
11        my $seq = Math::NumSeq::DigitProductSteps->new (values_type => 'count');
12        my ($i, $value) = $seq->next;
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DESCRIPTION

15       This is an iteration taking the product of the digits of a number until
16       reaching a single digit value.  The sequence values are the count of
17       steps, also called the multiplicative persistence.
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19           0,0,..0,0,1,1,..1,1,2,2,2,2,2,1,1,1,1,2,2,2,2,2,3,1,1,1,2,...
20           starting i=0
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22       For example i=39 goes 3*9=27 -> 2*7=14 -> 1*4=4 to reach a single
23       digit, so value=3 iterations.
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25       The "values_type => 'root'" gives the final digit reached by the steps,
26       which is called the multiplicative digital root.
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28           values_type => 'root'
29           0,1,2,...,9,0,1,...,9,0,2,4,6,8,0,2,4,6,8,0,3,6,9,2,5,8,...
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31       i=0 through i=9 are already single digits so their count is 0 and root
32       is the value itself.  Then i=10 to i=19 all take just a single
33       iteration to reach a single digit.  i=25 is the first to require 2
34       iterations.
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36       Any i with a 0 digit takes just one iteration to get to root 0.  Any i
37       like 119111 which is all 1s except for at most a single non-1 takes
38       just one iteration.  This includes the repunits 111..11.
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40   Radix
41       An optional "radix" parameter selects a base other than decimal.
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43       Binary "radix=>2" is not very interesting since the digit product is
44       always either 0 or 1.  i>=2 always takes just 1 iteration and has root
45       0 except for i=2^k-1 all 1s with root 1.
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FUNCTIONS

48       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
49       classes.
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51       "$seq = Math::NumSeq::DigitProductSteps->new ()"
52       "$seq = Math::NumSeq::DigitProductSteps->new (values_type => $str,
53       radix => $integer)"
54           Create and return a new sequence object.
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56   Random Access
57       "$value = $seq->ith($i)"
58           Return the sequence value, either count or final root value as
59           selected.
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61       "$bool = $seq->pred($value)"
62           Return true if $value occurs in the sequence.  For the count of
63           steps this means any integer "$value >= 0", or for a root any digit
64           "0 <= $value < radix".
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SEE ALSO

67       Math::NumSeq, Math::NumSeq::DigitProduct
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HOME PAGE

70       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

73       Copyright 2012, 2013, 2014 Kevin Ryde
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75       Math-NumSeq is free software; you can redistribute it and/or modify it
76       under the terms of the GNU General Public License as published by the
77       Free Software Foundation; either version 3, or (at your option) any
78       later version.
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80       Math-NumSeq is distributed in the hope that it will be useful, but
81       WITHOUT ANY WARRANTY; without even the implied warranty of
82       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
83       General Public License for more details.
84
85       You should have received a copy of the GNU General Public License along
86       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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90perl v5.28.0                      2014-06-29Math::NumSeq::DigitProductSteps(3)