++ed by:
Kevin Ryde
and 1 contributors

# NAME

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

# SYNOPSIS

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

# DESCRIPTION

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, ...``

# FUNCTIONS

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

``````    "all"
"odd"
"even"
"3k"
"squares"
"primes"``````