Kevin Ryde > Math-NumSeq-67 > Math::NumSeq::WoodallNumbers

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Module Version: 67   Source   Latest Release: Math-NumSeq-69

# 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.

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