Math::NumSeq::NumAronson -- numerical version of Aronson's sequence
use Math::NumSeq::NumAronson; my $seq = Math::NumSeq::NumAronson->new; my ($i, $value) = $seq->next;
This is a self-referential sequence by Cloitre, Sloane and Vandermast,
"Numerical Analogues of Aronson's Sequence", http://arxiv.org/abs/math.NT/0305308
The sequence begins
1, 4, 6, 7, 8, 9, 11, 13, ... starting i=1
Starting with 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, # 3 steps by 1 9, 11, 13, # 3 steps by 2 15, 16, 17, 18, 19, 20, # 6 steps by 1 21, 23, 25, 27, 29, 31, # 6 steps by 2 # 3*2^k steps by 1 # 3*2^k steps by 2
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.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::NumAronson->new ()
Create and return a new sequence object.
$value = $seq->ith($i)
Return the $i
th value in the sequence.
$bool = $seq->pred($value)
Return true if $value
occurs in the sequence.
Math::NumSeq, Math::NumSeq::Aronson
http://user42.tuxfamily.org/math-numseq/index.html
Copyright 2010, 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/>.