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


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


The Kolakoski sequence is

    i     = 1  2  3  4  5  6  7  8  9
    value = 1, 2, 2, 1, 1, 2, 1, 2, 2, ...          (OEIS A000002)

where the values are 1 or 2 and the run lengths of 1s or 2s are given by the sequence values themselves.

                |-| |--|  |--| |-||-| |--| 
                 1, 2, 2, 1, 1, 2, 1, 2, 2, ...      values
    run length   1    2     2   1  1   2    ...    lengths are values again


See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::Kolakoski->new ()

Create and return a new sequence object.


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


Math::NumSeq, Math::NumSeq::GolombSequence



Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020, 2021 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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