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Math::NumSeq::Pell -- Pell numbers
use Math::NumSeq::Pell; my $seq = Math::NumSeq::Pell->new; my ($i, $value) = $seq->next;
The Pell numbers
0, 1, 2, 5, 12, 29, 70, ... starting i=0
P(k) = 2*P(k-1) + P(k-2)
starting from i=0 values P(0)=0 and P(1)=1.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::Pell->new ()
Create and return a new sequence object.
($i, $value) = $seq->next()
Return the next index and value in the sequence.
$valueexceeds the range of a Perl unsigned integer the return is a
Math::BigIntto preserve precision.
$value = $seq->ith($i)
$i'th Pell number.
$bool = $seq->pred($value)
Return true if
$valueis a Pell number.
$i = $seq->value_to_i_estimate($value)
Return an estimate of the i corresponding to
The Pell numbers are a Lucas sequence and are a power
(1+sqrt(2))^i - (1-sqrt(2))^i P(i) = ----------------------------- exactly 2*sqrt(2)
Since abs(1-sqrt(2)) < 1 that term approaches zero, so taking logs the rest gives i roughly
log(value) + log(2*sqrt(2)) i ~= --------------------------- log(1+sqrt(2))
Copyright 2010, 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.
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