/ 
Math-NumSeq-75
River stage zero No dependents
/ Math::NumSeq::BaumSweet

NAME

Math::NumSeq::BaumSweet -- Baum-Sweet sequence

SYNOPSIS

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

DESCRIPTION

The Baum-Sweet 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 odd-length run of 0-bits, or 0 if it does.

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.

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

Create and return a new sequence object.

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 odd-length run of 0-bits.

$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/math-numseq/index.html

LICENSE

Copyright 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 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.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.