1Math::NumSeq::NumAronsoUns(e3r)Contributed Perl DocumentMaattiho:n:NumSeq::NumAronson(3)
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NAME

6       Math::NumSeq::NumAronson -- numerical version of Aronson's sequence
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SYNOPSIS

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

14       This is a self-referential sequence by Cloitre, Sloane and Vandermast,
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16           "Numerical Analogues of Aronson's Sequence",
17           <http://arxiv.org/abs/math.NT/0305308>
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19       The sequence begins
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21           1, 4, 6, 7, 8, 9, 11, 13, ...
22           starting i=1
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24       Starting with a(1)=1 the rule is "n is in the sequence iff a(n) is
25       odd".  The result is a uniform pattern 3 steps by 1 then 3 steps by 2,
26       followed by 6 steps by 1 and 6 steps by 2, then 12, 24, 48, etc.
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28           1,
29           4,
30           6,  7,  8,                   # 3 steps by 1
31           9,  11, 13,                  # 3 steps by 2
32           15, 16, 17, 18, 19, 20,      # 6 steps by 1
33           21, 23, 25, 27, 29, 31,      # 6 steps by 2
34                                        # 3*2^k steps by 1
35                                        # 3*2^k steps by 2
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37       In general
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39           numaronson(9*2^k-3+j) = 12*2^k - 3 + (3*j+abs(j))/2
40           where -3*2^k <= j < 3*2^k
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42       The (3*j+abs(j))/2 part is the step, going by 1 if j<=0 and by 2 if
43       j>0.
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FUNCTIONS

46       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
47       classes.
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49       "$seq = Math::NumSeq::NumAronson->new ()"
50           Create and return a new sequence object.
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52   Random Access
53       "$value = $seq->ith($i)"
54           Return the $ith value in the sequence.
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56       "$bool = $seq->pred($value)"
57           Return true if $value occurs in the sequence.
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SEE ALSO

60       Math::NumSeq, Math::NumSeq::Aronson
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HOME PAGE

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

66       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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68       Math-NumSeq is free software; you can redistribute it and/or modify it
69       under the terms of the GNU General Public License as published by the
70       Free Software Foundation; either version 3, or (at your option) any
71       later version.
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73       Math-NumSeq is distributed in the hope that it will be useful, but
74       WITHOUT ANY WARRANTY; without even the implied warranty of
75       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
76       General Public License for more details.
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78       You should have received a copy of the GNU General Public License along
79       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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83perl v5.36.0                      2022-07-22       Math::NumSeq::NumAronson(3)
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