1Math::NumSeq::KlarnerRaUdsoe(r3)Contributed Perl DocumenMtaatthi:o:nNumSeq::KlarnerRado(3)
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NAME

6       Math::NumSeq::KlarnerRado -- Klarner-Rado sequences
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SYNOPSIS

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

14       Start with 1, then for any k in the sequence then 2*k, 3*k+2 and 6*k+3
15       are in the sequence too.  Thus 1,2,4,5,8,9,etc.
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FUNCTIONS

18       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
19       classes.
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21       "$seq = Math::NumSeq::KlarnerRado->new ()"
22       "$seq = Math::NumSeq::KlarnerRado->new (start => $n)"
23           Create and return a new sequence object.
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25           The optional "start" parameter can start the sequence from a value
26           other than 1, which changes the sequence and in general bigger
27           values thin out the sequence.
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29       "$bool = $seq->pred($value)"
30           Return true if $value occurs in the sequence.
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FORMULAS

33   Predicate
34       Taking value mod 6 can say whether it's a descendant of one of the 2*k,
35       3*k+2, 6*k+3 forms, and thus give one or two reduced values to then
36       check for being in the sequence.
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38           value mod 6    descendant of       reduce to
39                0           2k               value/2
40                1           none
41                2           2k or 3k+2       value/2 and (value-2)/3
42                3           6k+3             (value-3)/6
43                4           2k               value/2
44                5           3k+2             (value-2)/3
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46       The reduction dividing out 2, 3 or 6 makes the test logarithmic, except
47       when 2mod6 gives two reduced values to check.
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SEE ALSO

50       Math::NumSeq
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HOME PAGE

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

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