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;
A sequence 1,2,2,1,1,2,1,etc, each run length being given successively by the sequence itself.
Starting from 1,2, at i=2 the values is 2, so there should be a run of two 2s. Then at i=3 value 2 means two 1s. Then at i=4 value 1 means a run of one 2. The value alternates between 1 and 2 and the sequence values themselves determine the run length to give that value, either 1 or 2.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
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.
Copyright 2011, 2012 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.
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