Kevin Ryde > Math-NumSeq > Math::NumSeq::WoodallNumbers

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Module Version: 71   Source  

NAME ^

Math::NumSeq::WoodallNumbers -- Woodall numbers i*2^i-1

SYNOPSIS ^

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

DESCRIPTION ^

The Woodall numbers i*2^i-1 starting from i=1,

    1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, ...

FUNCTIONS ^

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

$seq = Math::NumSeq::WoodallNumbers->new ()

Create and return a new sequence object.

Iterating

$seq->seek_to_i($i)

Move the current sequence position to $i. The next call to next() will return $i and corresponding value.

Random Access

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

Return $i * 2**$i - 1.

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

Return true if $value is a Woodall number, ie. is equal to i*2^i-1 for some i.

$i = $seq->value_to_i_floor($value)

Return the index i of $value or of the next Woodall number below $value.

$i = $seq->value_to_i_estimate($value)

Return an estimate of the i corresponding to $value.

FORMULAS ^

Value to i Estimate

An easy over-estimate is l=log2(value), which reverses value=2^l. It can be reduced by the bit length of that l as i=l-log2(l) to get closer.

SEE ALSO ^

Math::NumSeq, Math::NumSeq::CullenNumbers, Math::NumSeq::ProthNumbers

HOME PAGE ^

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

LICENSE ^

Copyright 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/>.

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