++ed by:
Kevin Ryde
and 1 contributors

# NAME

Math::NumSeq::NumAronson -- numerical version of Aronson's sequence

# SYNOPSIS

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

# DESCRIPTION

This is a self-referential sequence by Cloitre, Sloane and Vandermast, 1,4,6,7,8,9,11,13,etc, intended as a numerical version of Aronson's sequence (Math::NumSeq::Aronson).

``    http://arxiv.org/abs/math.NT/0305308``

Starting from a(1)=1 the rule is "n is in the sequence iff a(n) is odd". The result is a uniform pattern 3 steps by 1 then 3 steps by 2, followed by 6 steps by 1 and 6 steps by 2, then 12, 24, 48, etc.

``````    1,  4
6,  7,  8,  9,  11, 13
15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31``````

In general

``````    numaronson(9*2^k-3+j) = 12*2^k - 3 + (3*j+abs(j))/2
where -3*2^k <= j < 3*2^k``````

The (3*j+abs(j))/2 part is the step, going by 1 if j<=0 and by 2 if j>0.

# FUNCTIONS

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

`\$seq = Math::NumSeq::NumAronson->new ()`

Create and return a new sequence object.

## Random Access

`\$value = \$seq->ith(\$i)`

Return the `\$i`th value in the sequence.

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

Return true if `\$value` occurs in the sequence.

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

Copyright 2010, 2011, 2012 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/>.