1Math::NumSeq::ReverseAdUdsSetrepCso(n3t)ributed Perl DocMuamtehn:t:aNtuimoSneq::ReverseAddSteps(3)
2
3
4

NAME

6       Math::NumSeq::ReverseAddSteps -- steps of the reverse-add algorithm to
7       reach palindrome
8

SYNOPSIS

10        use Math::NumSeq::ReverseAddSteps;
11        my $seq = Math::NumSeq::ReverseAddSteps->new;
12        my ($i, $value) = $seq->next;
13

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.
18
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).
23
24       The default is to reverse decimal digits, or the "radix" parameter can
25       select another base.
26
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 ...)
33

FUNCTIONS

35       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
36       classes.
37
38       "$seq = Math::NumSeq::ReverseAddSteps->new ()"
39       "$seq = Math::NumSeq::ReverseAddSteps->new (radix => $r)"
40           Create and return a new sequence object.
41
42   Random Access
43       "$value = $seq->ith($i)"
44           Return the number of reverse-add steps required to reach a
45           palindrome.
46
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.
51

SEE ALSO

53       Math::NumSeq, Math::NumSeq::ReverseAdd, Math::NumSeq::CollatzSteps,
54       Math::NumSeq::JugglerSteps
55

HOME PAGE

57       <http://user42.tuxfamily.org/math-numseq/index.html>
58

LICENSE

60       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
61
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.
66
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.
71
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/>.
74
75
76
77perl v5.36.0                      2023-01-20  Math::NumSeq::ReverseAddSteps(3)
Impressum