Kevin Ryde > Math-NumSeq-71 > Math::NumSeq::KlarnerRado

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Module Version: 71   Source  

NAME ^

Math::NumSeq::KlarnerRado -- Klarner-Rado sequences

SYNOPSIS ^

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

DESCRIPTION ^

Start with 1, then for any k in the sequence then 2*k, 3*k+2 and 6*k+3 are in the sequence too. Thus 1,2,4,5,8,9,etc.

FUNCTIONS ^

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::KlarnerRado->new ()
$seq = Math::NumSeq::KlarnerRado->new (start => $n)

Create and return a new sequence object.

The optional start parameter can start the sequence from a value other than 1, which changes the sequence and in general bigger values thin out the sequence.

$bool = $seq->pred($value)

Return true if $value occurs in the sequence.

FORMULAS ^

Predicate

Taking value mod 6 can say whether it's a descendant of one of the 2*k, 3*k+2, 6*k+3 forms, and thus give one or two reduced values to then check for being in the sequence.

    value mod 6    descendant of       reduce to
         0           2k               value/2
         1           none             
         2           2k or 3k+2       value/2 and (value-2)/3
         3           6k+3             (value-3)/6
         4           2k               value/2
         5           3k+2             (value-2)/3

The reduction dividing out 2, 3 or 6 makes the test logarithmic, except when 2mod6 gives two reduced values to check.

SEE ALSO ^

Math::NumSeq

HOME PAGE ^

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE ^

Copyright 2011, 2012, 2013, 2014 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/>.

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