Math::NumSeq::PythagoreanHypots -- hypotenuses of Pythagorean triples
my $seq = Math::NumSeq::PythagoreanHypots->new;
my ($i, $value) = $seq->next;
This is integers occurring as the hypotenuse of a Pythagorean triple, ie. the C in A^2+B^2=C^2.
5, 10, 13, 15, 17, 20, ...
For example 13 is in the sequence because it occurs as 1^2+12^2 = 13^2.
It can be shown that this is all integers which have at least one prime factor of the form 4k+1.
Option pythagorean_type => "primitive" restricts to those hypotenuses occurring in primitive triples. For any triple A,B,C a multiple k*A,k*B,k*C is also a triple. The primitive triples are those where A,B have no common factor which could be divided out.
pythagorean_type => "primitive"
5, 13, 17, 25, 29, 37, ...
It can be shown these are integers comprised only of prime factors 4k+1. (For all triples at least one 4k+1 prime factor, and for primitive triples all 4k+1 prime factors.)
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::PythagoreanHypots->new ()
$seq = Math::NumSeq::PythagoreanHypots->new (pythagorean_type => $str)
Create and return a new sequence object.
$bool = $seq->pred($value)
Return true if $value occurs as a hypotenuse in a Pythagorean triple.
This calculation requires checking the prime factors of $value (to look for either one or all 4k+1). In the current code a hard limit of 2**32 is placed on $value in the interests of not going into a near-infinite loop.
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 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/>.
To install Math::NumSeq, copy and paste the appropriate command in to your terminal.
perl -MCPAN -e shell
For more information on module installation, please visit the detailed CPAN module installation guide.