NAME
Math::NumSeq::MephistoWaltz  Mephisto waltz sequence
SYNOPSIS
use Math::NumSeq::MephistoWaltz;
my $seq = Math::NumSeq::MephistoWaltz>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The Mephisto waltz sequence 0,0,1, 0,0,1, 1,1,0, etc, being the mod 2 count of ternary digit 2s in i. i=0 has no 2s so 0 and similarly i=1. Then i=2 has one 2 so 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
   copy   inverse 
++ ++ ++
The effect of the expansion is keep the initial third the same, append a copy of it, and an inverse of it 0 changed to 1 and 1 changed to 0.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
Random Access
$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.
FORMULAS
The calculation can be made in a powerof3 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.
SEE ALSO
Math::NumSeq, Math::NumSeq::DigitSumModulo
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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.
You should have received a copy of the GNU General Public License along with MathNumSeq. If not, see <http://www.gnu.org/licenses/>.