1Math::NumSeq::BaumSweetU(s3e)r Contributed Perl DocumentaMtaitohn::NumSeq::BaumSweet(3)
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NAME

6       Math::NumSeq::BaumSweet -- Baum-Sweet sequence
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SYNOPSIS

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

14       The Baum-Sweet sequence
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16           1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, ...
17           starting i=0
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19       where each value is 1 if the index i written in binary contains no odd-
20       length run of 0-bits, or 0 if it does.
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22           Leonard E. Baum and Melvin M. Sweet, "Continued Fractions of
23           Algebraic Power Series in Characteristic 2", Annals of Mathematics,
24           volume 103, number 3, May 1976, pages 593-610.
25           "/www.jstor.org/stable/1970953" in href="http:
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27       This sequence is the coefficients of a Laurent series which is the
28       unique solution to
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30           f(x)^3 + (1/x)*f(x) + 1 = 0
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32       and which they note has the bitwise interpretation above.  Their
33       interest was in certain continued fractions forms for the series.
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FUNCTIONS

36       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
37       classes.
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39       "$seq = Math::NumSeq::BaumSweet->new ()"
40           Create and return a new sequence object.
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42   Random Access
43       "$value = $seq->ith($i)"
44           Return the $i'th BaumSweet number, ie. 1 or 0 according to whether
45           $i is without or with an odd-length run of 0-bits.
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47       "$bool = $seq->pred($value)"
48           Return true if $value occurs in the sequence, which simply means 0
49           or 1.
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SEE ALSO

52       Math::NumSeq, Math::NumSeq::GolayRudinShapiro, Math::NumSeq::Fibbinary
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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, 2017, 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 v5.38.0                      2023-07-20        Math::NumSeq::BaumSweet(3)
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