NAME
Math::NumSeq::FibbinaryBitCount  number of bits in each fibbinary number
SYNOPSIS
use Math::NumSeq::FibbinaryBitCount;
my $seq = Math::NumSeq::FibbinaryBitCount>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The number of 1 bits in the i'th fibbinary number.
0, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, ...
starting i=0
For example i=9 is Fibbinary "1001" so value=2 for 2 1bits.
The count is 1 for the Fibonacci numbers, as they're "100..00" with a single 1bit in fibbinary.
Digit 0
Option digit => "0"
counts instead the 0bits
# digit=>"0" starting i=0
0, 0, 1, 2, 1, 3, 2, 2, 4, 3, 3, 3, 2, 5, 4, 4, 4, 3, 4, ...
i=0 is considered to be an empty set of digits, so it has value=0. This is the same as the DigitCount
sequence treats i=0.
Digit 00
Option digit => "00"
counts the 0bits which don't follow a 1bit, which is equivalent to "00" pairs (including overlapping pairs).
# digit=>"00" starting i=0
0, 0, 0, 1, 0, 2, 1, 0, 3, 2, 1, 1, 0, 4, 3, 2, 2, 1, 2, ...
For example i=42 is fibbinary "10010000" (42=34+8). It has value=4 for 4 0bits not counting the two which immediately follow the two 1bits. Or equivalently 4 "00" pairs
v vvv four 0s which don't follow a 1
i=42 10010000
^^ ^^ four "00" pairs, overlaps allowed
^^
^^
Fibbinary numbers by definition never have consecutive 1bits, so there's always a 0 following a 1. Excluding those leaves a count of genuinely skipped positions.
When passing the "00" option don't forget to quote it as a string, since a literal number 00 is an octal 0.
$seq = Math::NumSeq::FibbinaryBitCount>new (digit => "00"); # good
$seq = Math::NumSeq::FibbinaryBitCount>new (digit => 00); # bad
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::FibbinaryBitCount>new ()
$seq = Math::NumSeq::FibbinaryBitCount>new (digit => $str)

Create and return a new sequence object.
Random Access
$value = $seq>ith($i)

Return the bit count of the
$i
'th fibbinary number. $bool = $seq>pred($value)

Return true if
$value
occurs as a bit count, which simply means$value >= 0
.
SEE ALSO
Math::NumSeq, Math::NumSeq::Fibbinary, Math::NumSeq::DigitCount, Math::NumSeq::Fibonacci
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014 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/>.