Math::NumSeq::WoodallNumbers(3pm)

1Math::NumSeq::WoodallNuUmsbeerrsC(o3n)tributed Perl DocuMmaetnht:a:tNiuomnSeq::WoodallNumbers(3)
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NAME

6       Math::NumSeq::WoodallNumbers -- Woodall numbers i*2^i-1
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SYNOPSIS

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

14       The Woodall numbers i*2^i-1 starting from i=1,
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16           1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, ...
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FUNCTIONS

19       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
20       classes.
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22       "$seq = Math::NumSeq::WoodallNumbers->new ()"
23           Create and return a new sequence object.
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25   Iterating
26       "$seq->seek_to_i($i)"
27           Move the current sequence position to $i.  The next call to next()
28           will return $i and corresponding value.
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30   Random Access
31       "$value = $seq->ith($i)"
32           Return "$i * 2**$i - 1".
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34       "$bool = $seq->pred($value)"
35           Return true if $value is a Woodall number, ie. is equal to i*2^i-1
36           for some i.
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38       "$i = $seq->value_to_i_floor($value)"
39           Return the index i of $value or of the next Woodall number below
40           $value.
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42       "$i = $seq->value_to_i_estimate($value)"
43           Return an estimate of the i corresponding to $value.
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FORMULAS

46   Value to i Estimate
47       An easy over-estimate is l=log2(value), which reverses value=2^l.  It
48       can be reduced by the bit length of that l as i=l-log2(l) to get
49       closer.
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HOME PAGE

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

58       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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60       Math-NumSeq is free software; you can redistribute it and/or modify it
61       under the terms of the GNU General Public License as published by the
62       Free Software Foundation; either version 3, or (at your option) any
63       later version.
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65       Math-NumSeq is distributed in the hope that it will be useful, but
66       WITHOUT ANY WARRANTY; without even the implied warranty of
67       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
68       General Public License for more details.
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70       You should have received a copy of the GNU General Public License along
71       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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75perl v5.36.0                      2023-01-20   Math::NumSeq::WoodallNumbers(3)