1Math::NumSeq::HofstadteUrsFeirguCroen(t3r)ibuted Perl DoMcautmhe:n:tNautmiSoenq::HofstadterFigure(3)
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NAME

6       Math::NumSeq::HofstadterFigure -- sequence excludes its own first
7       differences
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SYNOPSIS

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

15       This is Douglas Hofstadter's "figure" sequence which comprises all
16       integers except those which are differences between its own successive
17       values,
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19           1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, 98, ...
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21       So for example at value=1 the next cannot be 2 because the difference
22       2-1=1 is already in the sequence, so value=3 with difference 3-1=2 is
23       next.  Then the next cannot be 4 since 4-3=1 is already in the
24       sequences, and likewise 5-3=2 and 6-3=3, so the next is value=7 with
25       7-3=4 not already in the sequence.
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27       The effect is that the sequence increments by 1,2,3,4, etc but
28       excluding values of the sequence itself.  This makes it close to the
29       Triangular numbers i*(i+1)/2, but incrementing by a little extra at the
30       places it skips its own values.
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32   Start Value
33       The optional "start => $value" can give the first value for the
34       sequence, instead of the default 1.  For example starting at 2
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36           2, 3, 7, 12, 18, 26, 35, 45, 56, ...
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38       or starting at 5
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40           5, 6, 8, 11, 15, 22, 31, 41, 53, 66, ...
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42       The differences are still the values not in the sequence, so for
43       example starting at 5 means the differences are 1, 2, 3, 4 before
44       skipping 5 and 6.
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46       In general the effect is to push the first skip up a bit, but still
47       settles down to grow roughly like the triangular numbers.
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49       The start > must be 1 or more.  If the start was 0 then the first value
50       and first difference would always be the same, contradicting the
51       conditions for the sequence.
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FUNCTIONS

54       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
55       classes.
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57       "$seq = Math::NumSeq::HofstadterFigure->new ()"
58       "$seq = Math::NumSeq::HofstadterFigure->new (start => $value)"
59           Create and return a new sequence object.
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SEE ALSO

62       Math::NumSeq, Math::NumSeq::Kolakoski
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HOME PAGE

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

68       Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
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70       Math-NumSeq is free software; you can redistribute it and/or modify it
71       under the terms of the GNU General Public License as published by the
72       Free Software Foundation; either version 3, or (at your option) any
73       later version.
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75       Math-NumSeq is distributed in the hope that it will be useful, but
76       WITHOUT ANY WARRANTY; without even the implied warranty of
77       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
78       General Public License for more details.
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80       You should have received a copy of the GNU General Public License along
81       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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85perl v5.28.1                      2014-06-29 Math::NumSeq::HofstadterFigure(3)
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