Math::NumSeq::Kolakoski(3pm)

1Math::NumSeq::KolakoskiU(s3e)r Contributed Perl DocumentaMtaitohn::NumSeq::Kolakoski(3)
2
3
4

NAME

6       Math::NumSeq::Kolakoski -- sequence of 1s and 2s its own run lengths
7

SYNOPSIS

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

DESCRIPTION

14       The Kolakoski sequence is
15
16           i     = 1  2  3  4  5  6  7  8  9
17           value = 1, 2, 2, 1, 1, 2, 1, 2, 2, ...          (OEIS A000002)
18
19       where the values are 1 or 2 and the run lengths of 1s or 2s are given
20       by the sequence values themselves.
21
22                       |-| |--|  |--| |-||-| |--|
23                        1, 2, 2, 1, 1, 2, 1, 2, 2, ...      values
24           run length   1    2     2   1  1   2    ...    lengths are values again
25

FUNCTIONS

27       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
28       classes.
29
30       "$seq = Math::NumSeq::Kolakoski->new ()"
31           Create and return a new sequence object.
32

FORMULAS

34       There's no need to keep the entire sequence, nor even the portion
35       between where i is up to and the values past that which those up to i
36       induce.  Instead the value at i is determined by the earlier value,
37       which is determined a yet earlier value, etc.  At each level only a
38       value and pending count need to be kept.  The levels required end up
39       being about log base 1.6 of the position i.
40

HOME PAGE

45       <http://user42.tuxfamily.org/math-numseq/index.html>
46

LICENSE

48       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020, 2021 Kevin Ryde
49
50       Math-NumSeq is free software; you can redistribute it and/or modify it
51       under the terms of the GNU General Public License as published by the
52       Free Software Foundation; either version 3, or (at your option) any
53       later version.
54
55       Math-NumSeq is distributed in the hope that it will be useful, but
56       WITHOUT ANY WARRANTY; without even the implied warranty of
57       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
58       General Public License for more details.
59
60       You should have received a copy of the GNU General Public License along
61       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
62
63
64
65perl v5.36.0                      2023-01-20        Math::NumSeq::Kolakoski(3)