Math::NumSeq::MephistoWaltz -- Mephisto waltz sequence
use Math::NumSeq::MephistoWaltz; my $seq = Math::NumSeq::MephistoWaltz->new; my ($i, $value) = $seq->next;
The Mephisto waltz sequence, being the mod 2 count of ternary digit 2s in i.
0,0,1, 0,0,1, 1,1,0, ... starting i=0
i=0 has no 2s so value=0, and likewise i=1 value=0. Then i=2 has one 2 so value=1.
The sequence can also be expressed as starting with 0 and repeatedly expanding
0 -> 0,0,1 1 -> 1,1,0
So
0 0,0,1 0,0,1, 0,0,1, 1,1,0, 0,0,1, 0,0,1, 1,1,0, 0,0,1, 0,0,1, 1,1,0, 1,1,0, 1,1,0, 0,0,1 | original | | copy | | inverse | +-----------------+ +-----------------+ +-----------------+
The effect of the expansion is keep the first third the same, append a copy of it, and append an inverse of it 0<->1.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::MephistoWaltz->new ()
Create and return a new sequence object.
$value = $seq->ith($i)
Return the $i
'th MephistoWaltz value, being the count mod 2 of the ternary digit 2s in $i
.
$bool = $seq->pred($value)
Return true if $value
occurs in the sequence, which simply means 0 or 1.
The calculation can be made in a power-of-3 base like 9, 27, 81, etc instead of just 3. For example in base 9 digits 2, 5, 6, 7 have a one (mod 2) ternary 2. These base 9 digits correspond to the 1s in the initial sequence 0,0,1, 0,0,1, 1,1,0 shown above.
Math::NumSeq, Math::NumSeq::DigitSumModulo
http://user42.tuxfamily.org/math-numseq/index.html
Copyright 2011, 2012, 2013, 2014 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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