NAME
Math::NumSeq::BaumSweet  BaumSweet sequence
SYNOPSIS
use Math::NumSeq::BaumSweet;
my $seq = Math::NumSeq::BaumSweet>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The BaumSweet sequence
1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, ...
starting i=0
where each value is 1 if the index i written in binary contains no oddlength run of 0bits, or 0 if it does.
Leonard E. Baum and Melvin M. Sweet, "Continued Fractions of Algebraic Power Series in Characteristic 2", Annals of Mathematics, volume 103, number 3, May 1976, pages 593610. "/www.jstor.org/stable/1970953" in href="http:
This sequence is the coefficients of a Laurent series which is the unique solution to
f(x)^3 + (1/x)*f(x) + 1 = 0
and which they note has the bitwise interpretation above. Their interest was in certain continued fractions forms for the series.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
Random Access
$value = $seq>ith($i)

Return the
$i
'th BaumSweet number, ie. 1 or 0 according to whether$i
is without or with an oddlength run of 0bits. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence, which simply means 0 or 1.
SEE ALSO
Math::NumSeq, Math::NumSeq::GolayRudinShapiro, Math::NumSeq::Fibbinary
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 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/>.