NAME
Math::NumSeq::SqrtEngel  Engel expansion of a square root
SYNOPSIS
use Math::NumSeq::SqrtEngel;
my $seq = Math::NumSeq::SqrtEngel>new (sqrt => 2);
my ($i, $value) = $seq>next;
DESCRIPTION
This is terms in the Engel expansion of a square root. The Engel expansion approaches the root by a series
1 1 1
sqrt(S) =  +  +  + ...
a[1] a[1]*a[2] a[1]*a[2]*a[3]
where each a[i] is chosen to make the term as big as possible without the total exceeding the target sqrt(S).
The sequence values are each successive a[i]. For example sqrt(2)
1 1 1 1 1
sqrt(2) =  +  +  +  +  + ...
1 1*3 1*3*5 1*3*5*5 1*3*5*5*16
is
1, 3, 5, 5, 16, etc
starting i=1
For a perfect square, the expansion is a finite sequence of 1s summing to the root. This is unlikely to be interesting, but works as a $seq
sequence.
sqrt(perfect square) = 1/1 + 1/1 + ... + 1/1
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::SqrtEngel>new (sqrt => $integer)

Create and return a new sequence object giving the Engel expansion terms of
sqrt($integer)
.
BUGS
The current code requires Math::BigInt
sqrt()
, which may mean BigInt 1.60 or higher (which comes with Perl 5.8.0).
SEE ALSO
Math::NumSeq, Math::NumSeq::SqrtDigits
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014, 2016, 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/>.