1Math::NumSeq::ReReplaceU(s3e)r Contributed Perl DocumentaMtaitohn::NumSeq::ReReplace(3)
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6 Math::NumSeq::ReReplace -- sequence of repeated replacements
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9 use Math::NumSeq::ReReplace;
10 my $seq = Math::NumSeq::ReReplace->new;
11 my ($i, $value) = $seq->next;
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14 This is a sequence by David Madore formed by repeatedly replacing every
15 N'th occurrence of a term with N.
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17 1, 2, 1, 2, 3, 3, 1, 2, 4, 4, 3, 4, ...
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19 As per
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21 David Madore, "have you seen this sequence?", sci.math.research, 24
22 Oct 2004,
23 <http://sci.tech-archive.net/Archive/sci.math.research/2004-10/0218.html>
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25 <http://www.madore.org/~david/.misc/seq.png>
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27 Stages
28 The generating procedure begins with all 1s,
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30 stage 0: 1,1,1,1,1,1,1,1,1,1,1,1,...
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32 Then every second 1 is changed to 2
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34 stage 1: 1,2,1,2,1,2,1,2,1,2,1,2,...
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36 Then every third 1 is changed to 3, and every third 2 changed to 3
37 also,
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39 stage 2: 1,2,1,2,3,3,1,2,1,2,3,3,...
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41 Then every fourth 1 becomes 4, every fourth 2 becomes 4, and every
42 fourth 3 becomes 4.
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44 stage 3: 1,2,1,2,3,3,1,2,4,4,3,4,...
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46 The replacement by N of every Nth is applied separately to the 1s, 2s,
47 3s etc remaining at each stage.
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49 The optional "stage => $n" parameter limits the replacements to a given
50 number of stages of the algorithm. The default -1 means unlimited.
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53 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
54 classes.
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56 "$seq = Math::NumSeq::ReReplace->new ()"
57 "$seq = Math::NumSeq::ReRound->new (stages => $integer)"
58 Create and return a new sequence object.
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60 "$bool = $seq->pred($value)"
61 Return true if $value occurs in the sequence. This merely means
62 integer "$value >= 1".
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65 Math::NumSeq, Math::NumSeq::ReRound
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68 <http://user42.tuxfamily.org/math-numseq/index.html>
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71 Copyright 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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73 Math-NumSeq is free software; you can redistribute it and/or modify it
74 under the terms of the GNU General Public License as published by the
75 Free Software Foundation; either version 3, or (at your option) any
76 later version.
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78 Math-NumSeq is distributed in the hope that it will be useful, but
79 WITHOUT ANY WARRANTY; without even the implied warranty of
80 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
81 General Public License for more details.
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83 You should have received a copy of the GNU General Public License along
84 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
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88perl v5.38.0 2023-07-20 Math::NumSeq::ReReplace(3)