Math::NumSeq::GolombSequence -- sequence is its own run lengths, 1 upwards


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


A sequence of integers with each run length being given by the sequence itself.

    1, 2,2, 3,3, 4,4,4, 5,5,5, 6,6,6,6,...

Starting from 1,2, at i=2 the value is 2, so there should be a run of two 2s. Then at i=3 value 2 means two 3s. Then at i=4 value 3 means a run of three 4s, and so on.

    Values     Run Length (is the sequence itself)
    1,            1
    2,2,          2
    3,3,          2
    4,4,4,        3
    5,5,5,        3
    6,6,6,6,      4
    ...          ...

Using Values

The default is to use all integers successively for the values. The using_values option can choose a different set of values. In each case those values from the sequence are the run lengths.

using_values => 'odd' uses only odd numbers,

    1, 3,3,3, 5,5,5, 7,7,7, 9,9,9,9,9, ...

using_values => 'even' uses only even numbers,

    2,2, 4,4, 6,6,6,6, 8,8,8,8, ...

using_values => '3k' uses only triples,

    3,3,3, 6,6,6, 9,9,9, 12,12,12,12,12,12, ...

using_values => 'squares' uses the squares,

    1, 4,4,4,4, 9,9,9,9, 16,16,16,16, 25,25,25,25, ...

using_values => 'primes' uses the primes,

    2,2, 3,3, 5,5,5, 7,7,7, 11,11,11,11,11, ...


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

$seq = Math::NumSeq::GolombSequence->new ()
$seq = Math::NumSeq::GolombSequence->new (using_values => $str)

Create and return a new sequence object. The using_values option as described above can be



Math::NumSeq, Math::NumSeq::Kolakoski

Math::NumSeq::Odd, Math::NumSeq::Even, Math::NumSeq::Squares, Math::NumSeq::Primes



Copyright 2011, 2012, 2013 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 <>.