1Math::NumSeq::ReverseAdUdsSetrepCso(n3t)ributed Perl DocMuamtehn:t:aNtuimoSneq::ReverseAddSteps(3)
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NAME

6       Math::NumSeq::ReverseAddSteps -- steps of the reverse-add algorithm to
7       reach palindrome
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SYNOPSIS

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

15       The number of steps to reach a palindrome by the digit "reverse and
16       add" algorithm.  For example the i=19 is 2 because 19+91=110 then
17       110+011=121 is a palindrome.
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19       At least one reverse-add is applied, so an i which is itself a
20       palindrome is not value 0, but wherever that minimum one step might end
21       up.  A repunit like 111...11 reverse-adds to 222...22 so it's always 1
22       (except in binary).
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24       The default is to reverse decimal digits, or the "radix" parameter can
25       select another base.
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27       The number of steps can be infinite.  In binary for example 3 = 11
28       binary never reaches a palindrome, and in decimal it's conjectured that
29       196 doesn't (and that is sometimes called the 196-algorithm).  In the
30       current code a hard limit of 100 is imposed on the search - perhaps
31       something better is possible.  (Some binary infinites can be recognised
32       from their bit pattern ...)
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FUNCTIONS

35       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
36       classes.
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38       "$seq = Math::NumSeq::ReverseAddSteps->new ()"
39       "$seq = Math::NumSeq::ReverseAddSteps->new (radix => $r)"
40           Create and return a new sequence object.
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42   Random Access
43       "$value = $seq->ith($i)"
44           Return the number of reverse-add steps required to reach a
45           palindrome.
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47       "$bool = $seq->pred($value)"
48           Return true if $value occurs in the sequence, which simply means
49           "$value >= 0" since any count of steps is possible, or "$value==-1"
50           for infinite.
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SEE ALSO

53       Math::NumSeq, Math::NumSeq::ReverseAdd, Math::NumSeq::CollatzSteps,
54       Math::NumSeq::JugglerSteps
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HOME PAGE

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

60       Copyright 2011, 2012, 2013, 2014 Kevin Ryde
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62       Math-NumSeq is free software; you can redistribute it and/or modify it
63       under the terms of the GNU General Public License as published by the
64       Free Software Foundation; either version 3, or (at your option) any
65       later version.
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67       Math-NumSeq is distributed in the hope that it will be useful, but
68       WITHOUT ANY WARRANTY; without even the implied warranty of
69       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
70       General Public License for more details.
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72       You should have received a copy of the GNU General Public License along
73       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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77perl v5.28.1                      2014-06-29  Math::NumSeq::ReverseAddSteps(3)
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